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Abstract Book / Conference Information

SPA OSAKA 201034th Conference on Stochastic Processes and Their Applications

September 6-10, 2010, Osaka, Japan

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Welcome to Osaka!

We are pleased to welcome you to the

34th Conference onStochastic Processes and Their Applications,

in Osaka from September 6th to 10th, 2010. The conference is organized under the auspices of the Bernoulli So-ciety for Mathematical Statics and Probability and co-sponsored by the Institute of Mathematical Statistics.It is a major annual meeting for researchers working in the field of Stochastic Processes and their Applications.

The conference covers a wide range of active research areas, in particular featuring 18 invited plenary lecturespresented by leading specialists. In addition, there will be a large variety of special sessions, consisting of threetalks each, and contributed sessions.

The conference is dedicated to the memory of Professor Kiyoshi Ito (Sep 7, 1915 - Nov 10, 2008), who wasone of the principal founders of modern theory on stochastic processes and a teacher of an entire generation ofJapanese probabilists. There will be two memorial lectures. Meanwhile the special issue of the journal “StochasticProcesses and their Applications,” Volume 120, Issue 5, dedicated to Professor Ito, was published. Elsevier kindlydeliver copies to participants.

We hope you will enjoy this meeting and your time in Osaka!

Ichiro ShigekawaHirofumi Osada

Bernoulli Societyfor Mathematical Statistics

and Probability

Institute of Mathematical Statistics

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Sponsors

The SPA meeting in Osaka 2010 would not have been possible without the generous support of our sponsors. Weare very grateful for the generous support provided by our corporate sponsors:

• Elsevier

• Osaka Convention & Tourism Bureau

• Sony Life Insurance Co., Ltd.

• Nippon Life Insurance Company

• Sumitomo Life Insurance Company

We are also very grateful for the generous support provided by the following organizations:

• Illinois Journal of Mathematics

• Global COE Program, Education and Research Hub for Mathematics-for-Industry

• Global COE Program, Fostering top leaders in mathematics – broadening the core and exploring newground

• Japan Society for the Promotion of ScienceGrant-in-Aid forScientific Research (S) (PI: Y. Giga)Scientific Research (A) (PI: H. Matsumoto)Scientific Research (A) (PI: S. Aida)Scientific Research (A) (PI: T. Funaki)Scientific Research (B) (PI: I. Shigekawa)Scientific Research (B) (PI: H. Osada)Scientific Research (B) (PI: T. Kumagai)Scientific Research (B) (PI: T. Shirai)Scientific Research (B) (PI: F. Hiroshima)Scientific Research (B) (PI: M. Takeda)Scientific Research (B) (PI: J. Kigami)Scientific Research (B) (PI: K. Kuwae)PI: Principal Investigator

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Scientific Committee:

Hirofumi OSADA, Chair (Kyushu University, Fukuoka)Maury BRAMSON (University of Minnesota, Minnesota)Krzysztof BURDZY (University of Washington, Seattle)Ana Bela CRUZEIRO (University of Lisbon, Lisbon)Tadahisa FUNAKI (University of Tokyo, Tokyo)Peter HALL (University of Melbourne, Melbourne)Claudia KLUPPELBERG (Technische Universitat Munchen, Munich)Terry LYONS (University of Oxford, Oxford)Avishai MANDELBAUM (Israel Institute of Technology, Haifa)Shige PENG (Shandong University, Jinan)Laurent SALOFF-COSTE (Cornell University, Ithaca)Gordon SLADE (University of British Columbia, Vancouver)Alain-Sol SZNITMAN (ETH Zurich, Zurich)Nizar TOUZI (Ecole Polytechnique, Palaiseau)S. R. Srinivasa VARADHAN (New York University, New York)Marc YOR (Universite Pierre et Marie Curie, Paris)

Organizing Committee:

Ichiro SHIGEKAWA, Chair (Kyoto University, Kyoto)Shigeki AIDA (Tohoku University, Sendai)Takashi KUMAGAI (Kyoto University, Kyoto)Hiroyuki MATSUMOTO (Yamagata University, Yamagata)Hiroshi SUGITA (Osaka University, Osaka)Setsuo TANIGUCHI (Kyushu University, Fukuoka)

Masanori HINO (Kyoto University, Kyoto)Hideo NAGAI (Osaka University, Osaka)Yoshiki OTOBE (Shinshu University, Matsumoto)Naomasa UEKI (Kyoto University, Kyoto)

Academic Secretaries:

Masanori HINO (Kyoto University, Kyoto)Yukio NAGAHATA (Osaka University, Osaka)Yuko YANO (Kyoto University, Kyoto)

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ContentsConference Information 1

General Information . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3Maps . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4Opening Ceremony . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 7Reception Party . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 7Ito Memorial Lectures . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 7Event of Bernoulli Society . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 8Excursion . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 8Banquet . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .8Closing Ceremony . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 8

Conference Schedule 9Schedule Table . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 11Sept. 6th (Mon.) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 12Sept. 7th (Tue.) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 12Sept. 8th (Wed.) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 13Sept. 9th (Thu.) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 13Sept. 10th (Fri.) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 14

Abstracts 37Plenary Talks . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 39Ito Memorial Lectures . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .43Invited Special Sessions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 44Organized Contributed Sessions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 64Open Contributed Sessions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 75Poster Sessions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 98

Registrants ??

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Conference Information

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General Information

Venue - Senri Life Science Center Building

1-4-2 Shinsenri-higashimachiToyonaka, Osaka560-0082 JAPAN

Access

By Subway (Kita-Osaka-Express)

Take a subway ”Mido-suji” line” bound for Senri-Chuo and get off at Senri-Chuo terminal station. Use the northexit to Senri Life Science Center. It is a 5-minute walk from Senri-Chuo (The Life Science Center building standsjust in front of the station; it will take several minutes to exit from the station).

From Kanasi International Airport (KIX)

[By JR]

Take JR Express ”Haruka” bound for Kyoto and get off at Shin-Osaka station. Change to the subway ”Mido-suji”line bound for Senri-Chuo and get off at Senri-Chuo terminal station. Use the north exit to Senri Life ScienceCenter. It is a 5-minute walk from Senri-Chuo.

[By Nankai Line]

Take Nankai Express ”Rapi:t” bound for Namba and get off at Namba terminal station. Change to the subway”Mido-suji” line bound for Senri-Chuo and get off at Senri-Chuo terminal station. Use the north exit to Senri LifeScience Center. It is a 5-minute walk from Senri-Chuo.

From Itami Airport (ITM, Osaka International Airport)

[By Monorail]

Take the monorail bound for Kadoma-shi and get off at Senri-Chuo. Senri Life Science Center is a 7-minute walkfrom Senri-Chuo.

From Narita International Airport (NRT)

[By rail]

Narita Express links Narita airport to Tokyo station. From Tokyo station, Shinkansen ”Nozomi” and ”Hikari”super express trains frequently depart to Shin-Osaka. It takes about 3 hours from Tokyo to Shin-Osaka. At Shin-Osaka station, change to the subway ”Mido-suji” line bound for Senri-Chuo and get off at Senri-Chuo terminalstation. Use the north exit to Senri Life Science Center. It is a 5-minute walk from Senri-Chuo. We, however,recommend to transit to Itami Airport.

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Convenience Store

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Senri Life Science Center Floor plan

Lifts

Science Hall

Life Hall

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Senri Room B

Lobby

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Men's Restroom Women's Restroom Restroom for Disabled

7th & 8th Floor

6th Floor

5th Floor

Conference Room 502, 503, 601, 602, 603, 604, 701, 801, 802

Life Hall (L.H.), Sceience Hall (S. H.)

Conference Office 501

Banquet Room Senri Room A & B (SR.A. & SR. B.)

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Opening CeremonyOn Monday morning (8:45) at Life Hall, after a short introduction by the hosts, the conference will be officiallyopened by Professor Marta Sanz-Sole (Barcelona, past chair of CCSP of the Bernoulli Society).

Reception PartyOn Monday night (18:30), all participants will be invited to a reception at Senri Room.

Ito Memorial Lectures

Kiyosi Ito (Sep. 7, 1915 – Nov. 10, 2008)

The theory of stochastic integral and stochastic differential equation due to Professor Kiyoshi Ito first appearedin “Zenkoku Sizyo Sugaku Danwakai-si” (i.e., Journ. Pan-Japan Math. Coll.) The journal was published in 1942from Osaka University. Since then, many works related to stochastic analysis were done by Professor Ito mainlyin Kyoto University, and he passed away in 2008. This time, the SPA conference is held in Osaka. So, in thisoccasion, we made a plan of special event in memory of Professor Ito, here in Osaka.

On Tuesday evening at Life Hall, there are two lectures in memory of Professor Kiyosi Ito:

16:05-16:50 Shinzo Watanabe“A review on the development of stochastic analysis”

17:00-17:45 Henry P. McKean“Reminiscence K. Ito, Some memories and some remarks on his mathematical style”

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Event of Bernoulli SocietyOn Wednesday morning (10:50–11:15) at Life Hall, for World Statistics Day, two speeches will be given by ISIPresident-Elect Jae C. Lee and BS President-Elect Edward Waymire. The title is “World Statistics Day: Thefuture of societies of mathematical statistics & probability.”

ExcursionA half day bus tour is arranged on Wednesday afternoon by Nippon Travel Agency. There are three plans asfollows:[A] Kiyomizu-dera & Kinkaku-ji,[B] Kinkaku-ji, Nishijin Textile Center & Nishiki-ichiba Market,[C] Kennin-ji Zazen Experience & Tea Ceremony at Kodai-ji.

BanquetThe banquet will take place on Wednesday night (19:00) at Senri Room. The charge for the banquet is 4,000 JPYfor registered participants.

Closing CeremonyOn Friday afternoon (16:00) at Life Hall, there will be a speech of Professor Victor Perez-Abreu (Guanajuato,President of Bernoulli Society).

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Conference Schedule

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SPA OSAKA 2010 Schedule Table

Lyons (IMS MedallionLecture)

Tuesday, 7thMonday, 6th Friday, 10thThursday, 9thWednesday, 8th

Opening

Event of BernoulliSociety

Lawler(Doob Lecture)

Wilson Sturm Miermont Hino

coffee break

Atar Kumagai Biskup Tang

coffee break coffee break coffee break coffee break

Rogers Hairer JacodSS04, SS06, SS13,SS26, SS27, CS04,CS07, CT06, CT11,CT16, CT18(Parallel sessions)

Khoshnevisan Jeanblanc Landim(Lévy Lecture)

lunchlunchlunch

lunch

lunch

Excursion

SS10, SS18, SS20,SS21, CS09, CS10,CS12, CT02, CT03,CT10, CT15(Parallel sessions)

SS09, SS12, SS14,SS23, SS25, CS08,CS14, CT07, CT09,CT12, CT19(Parallel sessions)

Taylor SS01, SS03, SS11,SS15, SS16, CS03,CS05, CS11, CT04,CT05, CT13, CT17,CT22(Parallel sessions)

coffee breakcoffee break

coffee breakPS II core time

PS I core time

Seppäläinen

Closing

SS05, SS07, SS17,SS24, CS01, CS02,CT20, CT23, CT25,CT26, CT27(Parallel sessions)

Reception Party(Senri Room)

Banquet(Senri Room)

Watanabe(Itô memorial lecture)

McKean(Itô memorial lecture)

SS02, SS08, SS19,SS22, CS06, CS13,CT01, CT08, CT14,CT21, CT24(Parallel sessions)

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On Monday, the conference office will open at 7:30 in the morning

SS: Invited Special SessionsCS: Organized Contributed SessionsCT: Open Contributed SessionsPS: Poster Sessions

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Conference ScheduleAbstract Page given in ( ) after Author’s Name

Monday, September 6th

8:45–9:00Opening(Life Hall)

9:00–9:45 Doob LectureGeometric, fractal, and multifractal properties of theSchramm-Loewner evolution (SLE)Gregory F. Lawler University of Chicago (p. 40)(Life Hall)

9:55–10:40On the non-degenerate slowdown diffusion regimeRami Atar Technion (p. 39)(Life Hall)

11:05–11:50Mathematical finance: the P&LChris Rogers University of Cambridge (p. 41)(Life Hall)

12:00–12:45On randomly-forced heat equationsDavar Khoshnevisan The University of Utah (p. 40)(Life Hall)

14:20–15:45Special Sessions and Contributed Sessions(Parallel sessions, see page 15)


18:30–Reception Party(Senri Room)

Tuesday, September 7th

9:00–9:45T.B.A.David Wilson Microsoft(Life Hall)

9:55–10:40Convergence of symmetric Markov chains on Zd

Takashi Kumagai Kyoto University (p. 40)(Life Hall)



16:05–16:50A review on the development of stochastic analysisShinzo Watanabe Kyoto University (p. 43)(Life Hall)

17:00–17:45Reminiscence K. Ito. Some memories and some re-marks on his mathematical styleHenry P. McKean Courant Institute of MathematicalSciences (p. 43)(Life Hall)

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Wednesday, September 8th

9:00–9:45Optimal transportation, gradient flows and Wasser-stein diffusionKarl-Theodor Sturm University of Bonn (p. 41)(Life Hall)

10:05–10:50 IMS Medallion LectureRough pathsTerence John Lyons University of Oxford (p. 41)(Life Hall)

10:50–11:15Event of Bernoulli SocietyISI President-Elect Jae C. Lee and BS President-Elect Edward WaymireWorld Statistics Day: The future of societies ofmathematical statistics & probability(Life Hall)

12:50–18:00Excursion

19:00–Banquet(Senri Room)

Thursday, September 9th

9:00–9:45Scaling limits of random planar mapsGregory Miermont Universite de Paris-Sud 11(p. 41)(Life Hall)

9:55–10:40Gradient models with non-convex interactionsMarek Biskup UCLA and University of South Bo-hemia (p. 39)(Life Hall)

11:05–11:50Spatially rough stochastic PDEsMartin Hairer University of Warwick (p. 39)(Life Hall)

12:00–12:45Construction and properties of a random time with agiven Azema supermartingaleMonique Jeanblanc Evry University (p. 40)(Life Hall)

14:20–15:05The integral geometry of random level setsJonathan Taylor Stanford University (p. 42)(Life Hall)

15:15–16:00Scaling exponents for 1+1-dimensional directedpolymersTimo O. Seppalainen University of Wisconsin-Madison (p. 41)(Life Hall)


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Friday, September 10th

9:00–9:45Martingale dimensions for self-similar fractalsMasanori Hino Kyoto University (p. 39)(Life Hall)

9:55–10:40On backward stochastic partial differential equa-tionsShanjian Tang Fudan University (p. 42)(Life Hall)

11:05–11:50Discretization of processes and applications to high-frequencyJean Jacod UPMC (Paris-6) (p. 40)(Life Hall)

12:00–12:45 Levy LectureMetastability of Markov processesClaudio Landim IMPA (p. 40)(Life Hall)


16:00–Closing(Life Hall)

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Monday, September 6th 14:20–15:45 (Parallel sessions)

Session title (Organizer)

Room 802 SS10: Potential Theory on Jump Processes (Kim)Room 601 SS18: Random Structure in Asymptotic Representation Theory (Hora)Life Hall SS20: SLE and Related Topics (Lawler)Science Hall SS21: Spatial Random Networks (van der Hofstad)Room 604 CS09: Some Analysis Related to Exponential (Geometric) Processes (Shieh)Room 603 CS10: Stochastic Differential Equations and their Graphs Applications (Smii)Room 502 CS12: Stochastic Optimal Stopping (Ano)Room 503 CT02: Brownian MotionRoom 602 CT03: BSDE and BSPDERoom 701 CT10: Mathematical Finance 1Room 801 CT15: Mathematical Statistics 1

SS: Invited Special SessionsCS: Organized Contributed SessionsCT: Open Contributed Sessions

(In the Open Contributed Sessions, the last speaker chairs the first talk; after this, each speaker chairs thenext talk by turns.)

SS10: Potential Theory on Jump ProcessesPanki Kim (Seoul National University)

14:20–14:45Heat and Weyl asymptotics for stable processesRodrigo Banuelos Purdue University (p. 44)

14:50–15:15Dirichlet heat kernel estimates for fractional Lapla-cian perturbed by gradient operatorZhen-Qing Chen University of Washington (p. 46)

15:20–15:45Transition probability densities of Levy processesRene L. Schilling TU Dresden (p. 59)

SS18: Random Structure in Asymptotic Rep-resentation TheoryAkihito Hora (Nagoya University)

14:20–14:45Higher order freeness and asymptotic representa-tions of unitary groupsBenoıt VP Collins University of Ottawa (p. 47)

14:50–15:15Asymptotics of characters and large Young dia-gramsValentin Feray LaBRI, CNRS Universite Bordeaux1 (p. 48)

15:20–15:45Real Wishart matrices and Haar-distributed orthog-onal matricesSho Matsumoto Nagoya University (p. 56)

SS20: SLE and Related TopicsGregory F. Lawler (University of Chicago)

14:20–14:45Connection probabilities and RSW-type bounds forthe two-dimensional FK Ising modelPierre Nolin Courant Institute, New York University(p. 57)

14:50–15:15A rate of convergence for loop-erased random walkto SLE(2)Michael Kozdron University of Regina (p. 53)

15:20–15:45Gaussian free field and conformal field theoryNam-Gyu Kang Seoul National University (p. 52)

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SS21: Spatial Random NetworksRemco van der Hofstad (Eindhoven University ofTechnology)

14:20–14:45Invariant random graphs with prescribed iid degreesMaria Deijfen Stockholm University (p. 47)

14:50–15:15Collective phenomena on random networksCristian Giardina Modena and Reggio Emilia Uni-versity (p. 49)

15:20–15:45Threshold networks with random weights and theirextension to spatial networksNaoki Masuda University of Tokyo (p. 56)

CS09: Some Analysis Related to Exponential(Geometric) ProcessesNarn-Rueih Shieh (National Taiwan University)

14:20–14:45Exponential (geometric) Levy process models inmathematical financeYoshio Miyahara Nagoya City University (p. 70)

14:50–15:15Exponential of stationary processesMuneya Matsui University of Tokyo (p. 70)

15:20–15:45Infinite products of exponential Levy-driven OU pro-cessesNarn-Rueih Shieh National Taiwan University(p. 72)

CS10: Stochastic Differential Equations andtheir Graphs ApplicationsBoubaker Smii (King Fahd University ofPetroleum and Minerals)

14:20–14:45Generalized Feynman graphs representation ofstochastic differential equations driven by LevynoiseBoubaker Smii King Fahd University of Petroleumand Minerals (p. 72)

14:50–15:15Shooting methods for numerical solution of linearand nonlinear stochastic boundary-value problemsArmando Arciniega The University of Texas at SanAntonio (p. 64)

15:20–15:45Maximum principle for controlled stochastic partialdifferential equationAbdulRahman Soliman Al-Hussein Qassim Uni-versity (p. 64)

CS12: Stochastic Optimal StoppingKatsunori Ano (Institute of Applied Mathematics)

14:20–14:45Pricing swing options by a dual approachYusuke Tashiro University of Tokyo (p. 73)

14:50–15:15Uncertain Markov decision processes with BayesianintervalsMasayuki Horiguchi Kanagawa University (p. 68)

15:20–15:45Odds theorem with multiple selection chancesKatsunori Ano Institute of Applied Mathematics(p. 64)

CT02: Brownian Motion

14:20–14:45Numerical approximation of second Neumanneigenfunctions in triangular domainsOana Rachieru Transilvania University of Brasov(p. 90)

14:50–15:15On collisions of Brownian particlesTomoyuki Ichiba University of California, SantaBarbara (p. 82)

15:20–15:45Skew products of one-dimensional diffusion pro-cesses and a spherical Brownian motionTomoko Takemura Kyoto University (p. 94)

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CT03: BSDE and BSPDE

14:20–14:45A BSDE approach to the sensitivity of the utilitymaximization problemMarkus Mocha Humboldt-Universitat zu Berlin(p. 87)

14:50–15:15Measure solutions of BSDEs and a Feynman-KacformulaJianing Zhang Humboldt-Universitat zu Berlin(p. 97)

15:20–15:45On the Cauchy problem for degenerate backwardstochastic partial differential equations in SobolevspacesKai Du Fudan University (p. 78)

CT10: Mathematical Finance 1

14:20–14:45A new approach to pricing European Union emis-sion allowance futuresAnna Nazarova University of Duisburg-Essen(p. 87)

14:50–15:15Averaging principle for an order book modelMichael Christoph Paulsen Humboldt Universityof Berlin (p. 88)

15:20–15:45Analytical solution for expected loss of a collateral-ized loan under a quadratic Gaussian default inten-sity processToshinao Yoshiba Bank of Japan (p. 97)

CT15: Mathematical Statistics 1

14:20–14:45Lifetime inference of skew-Wiener linear degrada-tion modelsChien-Yu Peng Institute of Statistical Science,Academia Sinica (p. 89)

14:50–15:15Residuals and goodness-of-fit tests for stationarymarked Gibbs point processesFrederic Lavancier Universite de Nantes (p. 85)

15:20–15:45On the Markov transition kernel for first-passagepercolation on the ladderEckhard Schlemm Technische Universitat Munchen(p. 92)

18

Monday, September 6th 16:15–18:10 (Parallel sessions)


Life Hall SS05: Financial Mathematics (Bouchard and Zariphopoulou)Room 802 SS07: Levy processes: Recent Developments (Kluppelberg)Science Hall SS17: Random Media and Related Topics (Sidoravicius)Room 601 SS24: Stochastic Models in Neuroscience (Thieullen)Room 502 CS01: Affine Processes and Applications (Keller-Ressel)Room 503 CS02: Branching Processes and their Applications (Gonzalez and del Puerto)Room 602 CT20: Queueing TheoryRoom 603 CT23: SDE and SPDERoom 801 CT25: Stochastic AnalysisRoom 701 CT26: Stochastic Controls and Related TopicsRoom 604 CT27: Stochastic Network



SS05: Financial MathematicsBruno Bouchard (Universite Paris-Dauphine) andThaleia Zariphopoulou (University of Oxford andUniversity of Texas, Austin)

16:15–16:40New perspectives on the HJB equation arising inportfolio choice in incomplete marketsSergey Nadtochiy University of Oxford (p. 57)

16:45–17:10Optimal investment on finite horizon with randomdiscrete order flow in illiquid marketsMihai Sırbu University of Texas (p. 59)

17:15–17:40No asymptotic arbitrage in models with transactioncosts and production capacitiesBruno Bouchard CEREMADE, University Paris-Dauphine CREST, ENSAE (p. 45)

SS07: Levy Processes: Recent DevelopmentsClaudia Kluppelberg (TU Munchen)

16:15–16:40On fractional Levy processesChristian Bender Saarland University (p. 44)

16:45–17:10Distributional properties of stationary solutions ofsome generalised Ornstein–Uhlenbeck processesAlexander M. Lindner TU Braunschweig (p. 54)

17:15–17:40More about limits of nested subclasses of classes ofinfinitely divisible distributionsMakoto Maejima Keio University (p. 55)

17:45–18:10The role of the arcsine distribution in infinite divisi-bilityVictor Perez-Abreu Center for Research in Mathe-matics CIMAT (p. 58)

19

SS17: Random Media and Related TopicsVladas Sidoravicius (CWI and IMPA)

16:15–16:40The self-dual point of the two-dimensional random-cluster model is critical for q ≥ 1Vincent Beffara UMPA - ENS Lyon (p. 44)

16:45–17:10Random pinning model: the issue of disorder rele-vanceHubert Lacoin Universita di Roma Tre (p. 54)

17:15–17:40Some aspects of directed edge reinforced randomwalksChristophe Sabot Universite Lyon 1 (p. 59)

17:45–18:10T.B.A.Gerard Ben Arous New York University

SS24: Stochastic Models in NeuroscienceMichele Thieullen (Universite Pierre et MarieCurie)

16:15–16:40Stochastic differential equations with boundarynoiseStefano Bonaccorsi University of Trento (p. 45)

16:45–17:10Synchrony-breaking and rare events in stochasticneuronal networksLee DeVille University of Illinois (p. 47)

17:15–17:40Modelization of membrane potential and informationtransmission in large systems of neuronsReinhard Hoepfner University of Mainz (p. 50)

17:45–18:10Piecewise deterministic processes and intrinsic fluc-tuations of neuronal activityMichele Marie Thieullen Universite Pierre et MarieCurie-Paris 6 (p. 60)

CS01: Affine Processes and ApplicationsMartin Keller-Ressel (Swiss Federal Institute ofTechnology)

16:15–16:40On strong solutions of positive definite jump-diffusionsEberhard Mayerhofer Vienna University of Eco-nomics and Business (p. 70)

16:45–17:10Affine processes on symmetric conesChrista Cuchiero ETH Zuerich (p. 65)

17:15–17:40A characterization of the martingale property of ex-ponentially affine processesJohannes Muhle-Karbe University of Vienna(p. 70)

CS02: Branching Processes and their Appli-cationsMiguel Gonzalez and Ines del Puerto (Universityof Extremadura)

16:15–16:40Branching structure for an (L-1) random walk in ran-dom environment and its applicationsWenming Hong Beijing Normal University (p. 68)

16:45–17:10Y-linked bisexual branching processes with blindchoice of mates: Bayesian inference throughMCMC methodsMiguel Gonzalez University of Extremadura (p. 66)

17:15–17:40On controlled branching processes in varying envi-ronmentInes Maria del Puerto University of Extremadura(p. 65)

CT20: Queueing Theory

16:15–16:40Shadow-routing based control of flexible multi-server pools in overloadTolga Tezcan University of Rochester (p. 94)

20

16:45–17:10Non-identifiability of the two-state Markovian arrivalprocessJosefa Ramirez Cobo IMUS (Institute of Mathe-matics, University of Seville) (p. 90)

17:15–17:40Multiscale diffusion approximations for stochasticnetworks in heavy trafficXin Liu University of North Carolina at Chapel Hill(p. 86)

17:45–18:10Interararrival time distribution for a non-Markovianarrival processMine Caglar Koc University (p. 76)

CT23: SDE and SPDE

16:15–16:40Ergodicity and density asymptotics of complex diffu-sion processes with quadratic driftDavid Paul Herzog The University of Arizona(p. 81)

16:45–17:10Regularity of the diffusion semigroup with Dirichletboundary conditionShigeo Kusuoka The University of Tokyo (p. 84)

17:15–17:40The equivalence of stochastic differential equationsand martingale problemsThomas G Kurtz University of Wisconsin-Madison(p. 84)

17:45–18:10Ergodicity of infinite dimensional stochastic differen-tial equations with jump noisesBin Xie Shinshu University (p. 96)

CT25: Stochastic Analysis

16:15–16:40An algebraic approach to the Cameron-Martin-Maruyama-Girsanov formulaTakafumi Amaba Ritsumeikan University (p. 75)

16:45–17:10On integro-differential operators: Conservativenessand Feller propertyYuichi Shiozawa Okayama University (p. 92)

17:15–17:40Lp-approximations of stochastic integrals andweighted BMOStefan Geiss University of Innsbruck (p. 79)

17:45–18:10Random time with a given Azema supermartingale:A multiplicative system approachLibo Li University of Sydney (p. 85)

CT26: Stochastic Controls and Related Topics

16:15–16:40Large time behavior of solutions of Hamilton-Jacobi-Bellman equations with quadratic nonlinearity ingradientsNaoyuki Ichihara Hiroshima University (p. 82)

16:45–17:10Optimal control of trading algorithms: a general im-pulse control approachNgoc-Minh Dang CEREMADE, University ParisDauphine (p. 77)

17:15–17:40Card counting in continuous timePatrik Andersson Stockholm University (p. 75)

17:45–18:10Convex risk measures on Orlicz spaces: inf-convolution and shortfallTakuji Arai Keio University (p. 75)

CT27: Stochastic Network

16:15–16:40The multiple scaling approximation in a heat shockmodel of E.coliHye Won Kang University of Minnesota (p. 83)

16:45–17:10Weak law for number of edges on a spherical sur-faceBhupendra Gupta Indian Institute of Informa-tion Technology -Desigm and Manufacturing-Jabalpur(p. 80)

17:15–17:40The on-off network traffic model under intermediatescalingClement Dombry Universite de Poitiers (p. 78)

21

17:45–18:10Stochastically perturbed gene regulatory networksIrina Shlykova Norwegian University of Life Sci-ences (p. 93)

22

Tuesday, September 7th 11:05–12:30 (Parallel sessions)


Room 604 SS04: Excursion Theory and Applications (Fukushima and Yano)Room 601 SS06: Functional Inequalities and Related Topics (Wang)Room 802 SS13: Probabilistic Numerical Methods for PDEs (Touzi)Life Hall SS26: Stochastic Processes in Physics (Hara)Science Hall SS27: Stochastic Process Models in Genetics (Griffiths)Room 502 CS04: Non-Local Operators and Related Random Processes (Lorinczi)Room 503 CS07: SDE with Jumps I (Pavlyukevich and Simon)Room 603 CT06: Interacting Systems and Statistical Mechanics 1Room 701 CT11: Mathematical Finance 2Room 801 CT16: Mathematical Statistics 2Room 602 CT18: Optimal Transportation, Random Walks on Graphs



SS04: Excursion Theory and ApplicationsMasatoshi Fukushima (Osaka University) andYuko Yano (Kyoto University)

11:05–11:30Applications of excursion theory to construction anduniqueness of stochastic processesKrzysztof Burdzy University of Washington (p. 46)

11:35–12:00Extremality of excursion measure and of σ-finitemeasure unifying penalisationsKouji Yano Kobe University (p. 62)

12:05–12:30Shift-monotonicity and infinite divisibility for regen-erative setsPatrick Joseph Fitzsimmons University of Cali-fornia San Diego (p. 48)

SS06: Functional Inequalities and RelatedTopicsFeng-Yu Wang (Swansea University)

11:05–11:30COH formula and Dirichlet Laplacians on small do-mains of pinned path spacesShigeki Aida Tohoku University (p. 44)

11:35–12:00Lyapunov conditions for functional inequalitiesArnaud Guillin Universite Blaise Pascal (p. 50)

12:05–12:30Strong ergodicity and spectral property for MarkovprocessesYong-Hua Mao Beijing Normal University (p. 55)

SS13: Probabillistic Numerical Methods forPDEsNizar Touzi (Ecole Polytechnique)

11:05–11:30Optimal stopping of piecewise deterministic MarkovprocessesFrancois Dufour INRIA Bordeaux Sud-Ouest(p. 47)

23

11:35–12:00An application of the Kusuoka-Lyons-Victoir cuba-ture method to the numerical solution of semilinearPDEsDan Crisan Imperial College London (p. 47)

12:05–12:30Monte Carlo Methods for high dimensional BSDEsand PDEsJianfeng Zhang University of Southern California(p. 63)

SS26: Stochastic Processes in PhysicsTakashi Hara (Kyushu University)

11:05–11:30Lace expansion in the past and futureAkira Sakai Hokkaido University (p. 59)

11:35–12:00Dissipative Abelian sandpiles and rate of conver-genceAntal A Jarai University of Bath (p. 51)

12:05–12:30Phase transition in kinetically constrained modelsThierry Bodineau Ecole Normale Superieure (p. 45)

SS27: Stochastic Process Models in GeneticsRobert Griffiths (University of Oxford)

11:05–11:30Computing likelihoods under multiple-merger coa-lescentsMatthias Birkner University Mainz (p. 44)

11:35–12:00A coalescent dual process in a Cannings model withgenic selection, and the Lambda coalescent limitRobert Charles Griffiths University of Oxford(p. 50)

12:05–12:30Evolution in a spatial continuumJerome Kelleher University of Edinburgh (p. 53)

CS04: Non-Local Operators and Related Ran-dom ProcessesJozsef Lorinczi (Loughborough University)

11:05–11:30Hitting distributions of stable and related processesMichal Ryznar Wroclaw University of Technology(p. 71)

11:35–12:00Hitting half-spaces by Bessel-Brownian diffusionsJacek Malecki University of Angers and WroclawUniversity of Technology (p. 69)

12:05–12:30Schroedinger perturbations of transition densitiesKrzysztof Bogdan Wroclaw University of Technol-ogy (p. 65)

CS07: SDE with Jumps IIlya Pavlyukevich (Friedrich Schiller University ofJena) and Thomas Simon (Universite de Lille 1)

11:05–11:30Stationary solutions of generalised Ornstein-Uhlenbeck processesAnita Diana Behme TU Braunschweig (p. 64)

11:35–12:00The lent particle method and its applicationsLaurent Denis University of Evry (p. 66)

12:05–12:30Stochastic equations and Fleming-Viot flowsZenghu Li Beijing Normal University (p. 69)

CT06: Interacting Systems and Statistical Me-chanics 1

11:05–11:30Existence and uniqueness of random gradientstatesCodina Cotar Technische Universitat Muenchen(p. 76)

11:35–12:00Fractional Fokker-Planck equation for subdiffusionwith space-and-time-dependent driftPeter Straka University of New South Wales (p. 93)

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12:05–12:30Annealed critical curve of a disordered pinningmodel with finite range correlationsJulien Poisat Universite Lyon 1 (p. 89)


11:05–11:30A model for multiscaling and clustering of volatilityin financial indexesPaolo Dai Pra Universita di Padova (p. 77)

11:35–12:00On the Fatou property for quasiconvex functionsRanja Reda Vienna University of Technology (p. 91)

12:05–12:30Large liquidity expansion of the super-hedging costsDylan Possamaı Ecole Polytechnique (p. 90)


11:05–11:30Profile monitoring via penalized spline regressionLongcheen Huwang National Tsing Hua University(p. 81)

11:35–12:00Misspecification analyses of Gamma with inverseGaussian processesSheng Tsaing Tseng National Tsing-Hua Univer-sity (p. 95)

12:05–12:30Estimation in linear regression measurement errormodels for processes with uncorrelated incrementsTiee-Jian Wu National Cheng-Kung University(p. 96)

CT18: Optimal Transportation, Random Walkson Graphs

11:05–11:30Fair allocation via optimal transportationMartin Otto Josef Huesmann University of Bonn(p. 81)

11:35–12:00Large deviations on nilpotent covering graphsRyokichi Tanaka Kyoto University (p. 94)

12:05–12:30Duality on gradient estimates and Wasserstein con-trolsKazumasa Kuwada Ochanomizu University (p. 84)

25

Tuesday, September 7th 14:10–15:35 (Parallel sessions)


Room 601 SS09: Mathematical Populations Genetics (Baake)Room 802 SS12: Probabilistic Methods for Solving Stochastic and Deterministic PDE’s (Crisan)Room 801 SS14: Probability and Geometry (Kuwae)Life Hall SS23: Stochastic Analysis on Large Scale Interacting Systems (Deuschel)Science Hall SS25: Stochastic Networks (Ramanan)Room 502 CS08: SDE with Jumps II (Pavlyukevich and Simon)Room 503 CS14: Stochastic Processes in Actuarial Modelling (Willmot)Room 603 CT07: Interacting Systems and Statistical Mechanics 2Room 602 CT09: Limit Theorems and Random DynamicsRoom 701 CT12: Mathematical Finance 3Room 604 CT19: Probability Distribution



SS09: Mathematical Population GeneticsEllen Baake (Universitat Bielefeld)

14:10–14:35The symbiotic branching model: Moment spectrum,longtime-behaviour and width of the interfaceJochen Blath TU Berlin (p. 45)

14:40–15:05Spatial Lambda-Fleming-Viot process and associ-ated genealogiesAmandine Veber University Paris-Sud 11 (p. 61)

15:10–15:35Single–crossover recombination and ancestral re-combination treesUte von Wangenheim Bielefeld University (p. 62)

SS12: Probabilistic Methods for SolvingStochastic and Deterministic PDEsDan Crisan (Imperial College London)

14:10–14:35Accelerated numerical schemes for deterministicand stochastic PDEsIstvan Gyongy University of Edinburgh (p. 50)

14:40–15:05On generalized Malliavin calculusBoris L Rozovsky Brown University (p. 58)

15:10–15:35Second order backward SDEsNizar Touzi Ecole Polytechnique (p. 61)

SS14: Probability and GeometryKazuhiro Kuwae (Kumamoto University)

14:10–14:35Concentration of measure phenomenon and eigen-values of LaplacianKei Funano Kumamoto University (p. 49)

14:40–15:05Displacement convexity of generalized relative en-tropiesShin-ichi Ohta Kyoto University (p. 58)

15:10–15:35Comparison geometry of the Bakry-Emery Riccicurvature on complete Riemannian manifoldsXiangdong Li Chinese Academy of Sciences (p. 54)

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SS23: Stochastic Analysis on Large Scale In-teracting SystemsJean-Dominique Deuschel (TU Berlin)

14:10–14:35Effective velocity for interfaces in a random environ-mentNicolas P Dirr University of Bath (p. 47)

14:40–15:05Fluctuations of the Ginzburg-Landau model and uni-versality for SLE(4)Jason P. Miller Stanford University (p. 57)

15:10–15:35Scaling limits of self-interacting random walks anddiffusionsBalint Toth Budapest University of Technology(p. 60)

SS25: Stochastic NetworksKavita Ramanan (Brown University)

14:10–14:35A stochastic model of coupled enzymatic process-

ingRuth Williams University of California, San Diego(p. 62)

14:40–15:05Scaling limits for critical epidemics and randomgraphsJohan van Leeuwaarden TU Eindhoven and EU-RANDOM (p. 61)

15:10–15:35Interpolation method and scaling limits in sparserandom graphsDavid Gamarnik MIT (p. 49)

CS08: SDE with Jumps IIIlya Pavlyukevich (Friedrich Schiller University ofJena) and Thomas Simon (Universite de Lille 1)

14:10–14:35On estimating SDE with jumpsHiroki Masuda Kyushu University (p. 69)

14:40–15:05Cylindrical Levy processes in Banach spacesMarkus Riedle University of Manchester (p. 71)

15:10–15:35Sensitivity and hypoellipticity for jump processesAtsushi Takeuchi Osaka City University (p. 72)

CS14: Stochastic Processes in Actuarial Mod-ellingGordon Willmot (University of Waterloo)

14:10–14:35Distributional analysis of a generalization of thePolya processGordon Willmot University of Waterloo (p. 73)

14:40–15:05General structures of a class of stochastic modelswith two-sided jumpsEric Cheung University of Hong Kong (p. 65)

15:10–15:35Refinements of the two-sided bounds for renewalequationsJae-Kyung Woo University of Waterloo (p. 74)

CT07: Interacting Systems and Statistical Me-chanics 2

14:10–14:35Hydrodynamic limit for exclusion processes with ve-locityMakiko Sasada The University of Tokyo (p. 91)

14:40–15:05Duality and hidden symmetries in interacting parti-cle systemsKiamars Vafayi Leiden University (p. 95)

15:10–15:35Spatial random permutations and Poisson-DirichletdistributionVolker Betz University of Warwick (p. 76)

CT09: Limit Theorems and Random Dynamics

14:10–14:35Quenched limit theoremsDalibor Volny Universite de Rouen (p. 95)

14:40–15:05On the central limit theorem for trimmed r.v.’sIstvan Berkes Graz University of Technology (p. 75)

27

15:10–15:35Cooperation principle and disappearance of chaosin random complex dynamicsHiroki Sumi Osaka University (p. 93)


14:10–14:35Active portfolio selection: Outperforming a bench-mark portfolioDaniel Michelbrink The University of Nottingham(p. 87)

14:40–15:05Constrained portfolio choices in the decumulationphase of a pension planFausto Gozzi Luiss University (p. 80)

15:10–15:35Volatility in the Black-Scholes and other formulaeKais Hamza Monash University (p. 81)

CT19: Probability Distribution

14:10–14:35On the mixture of the displaced exponential distribu-tion and the uniform distributionEpimaco, Jr. Alamares Cabanlit Mindanao StateUniversity (p. 76)

14:40–15:05On the joint distribution of two quantilesYuri Imamura Ritsumeikan University (p. 82)

15:10–15:35Transition densities of transformations of Ito diffu-sionsSanae Rujivan Walailak University (p. 91)

28

Thursday, September 9th 16:25–18:20 (Parallel sessions)


Room 601 SS02: Determinantal Processes and Related Topics (Shirai)Life Hall SS08: Mathematical Finance and Stochastic Control (Sheu)Science Hall SS19: Rough Paths (Lyons)Room 802 SS22: Statistical Inference for Stochastic Processes (Yoshida)Room 502 CS06: Quantum Walks (Konno)Room 604 CS13: Stochastic Partial Differential Equations and Related Topics (Tappe)Room 602 CT01: Branching Processes and Other Stochastic ProcessesRoom 503 CT08: Levy ProcessesRoom 701 CT14: Mathematical Finance and Risk AnalysisRoom 603 CT21: Random MediaRoom 801 CT24: SPDE and its Applications



SS02: Determinantal Processes and RelatedTopicsTomoyuki Shirai (Kyushu University)

16:25–16:50Random point processes and Wigner matricesAlexander B. Soshnikov University of California atDavis (p. 60)

16:55–17:20The critical Z-invariant Ising model via dimersCedric Boutillier UPMC Paris 6 – Ecole NormaleSuperieure (p. 46)

17:25–17:50Limit of characteristic polynomials of a random ma-trixManjunath Krishnapur Indian Institute of Science(p. 53)

SS08: Mathematical Finance and StochasticControlShuenn-Jyi Sheu (Academia Sinica)

16:25–16:50Robust utility maximization for Levy market modelsDaniel Hernandez Centro de Investigacion enMatematicas (p. 50)

16:55–17:20Robust utility maximization on an infinite time hori-zonThomas Knispel Leibniz University Hannover(p. 53)

17:25–17:50An impulse control approach to optimal order exe-cution with market price impactHuyen Pham University Paris Diderot (p. 58)

17:55–18:20On nearly optimal strategies for risk-sensitive port-folio optimization on infinite horizonJun Sekine Osaka University (p. 59)

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SS19: Rough PathsTerry Lyons (University of Oxford)

16:25–16:50Evolving communities with individual preferencesThomas Cass University of Oxford (p. 46)

16:55–17:20A new pathwise theory of SPDEsPeter Karl Friz TU and WIAS Berlin (p. 49)

17:25–17:50Laplace-type asymptotics for rough differentialequation driven by fractional Brownian motionYuzuru Inahama Nagoya University (p. 51)

SS22: Statistical Inference for Stochastic Pro-cessesNakahiro Yoshida (University of Tokyo)

16:25–16:50On the goodness of fit tests for ergodic diffusion pro-cessesYury A. Kutoyants University of Maine (p. 54)

16:55–17:20Unlimited liabilities, reserve capital requirementsand the taxpayer put optionErnst Wilhelm Eberlein University of Freiburg(p. 48)

17:25–17:50Statistical estimation of the volatility for a stochasticdifferential equationMasayuki Uchida Osaka University (p. 61)

CS06: Quantum WalksNorio Konno (Yokohama National University)

16:25–16:50Spectral methods for quantum random walksF. Alberto Grunbaum University of California,Berkeley (p. 67)

16:55–17:20Applications of spectral methods for quantum ran-dom walksLuis Velazquez Universidad de Zaragoza (p. 73)

17:25–17:50Limit theorems and localization for quantum walkson graphsNorio Konno Yokohama National University (p. 69)

CS13: Stochastic Partial Differential Equa-tions and Related TopicsStefan Tappe (ETH Zurich)

16:25–16:50Support theorem for SPDE and its application toHJM modelToshiyuki Nakayama Mitsubishi UFJ Morgan Stan-ley Securities Co., Ltd. (p. 70)

16:55–17:20Invariant manifolds with boundary for jump-diffusionsStefan Tappe ETH Zurich (p. 73)

17:25–17:50Relation between stochastic integrals and the ge-ometry of Banach spacesBarbara Rudiger Bergische Universitat Wuppertal(p. 71)

CT01: Branching Processes and OtherStochastic Processes

16:25–16:50A stochastic SIS epidemic with demography: initialstages and time to extinctionDavid Lindenstrand Stockholm University (p. 86)

16:55–17:20Some asymptotic results for near critical branchingprocessesDominik Reinhold University of North Carolina atChapel Hill (p. 91)

17:25–17:50Estimation of distribution function in marked pointprocessesZbynek Pawlas Charles University in Prague (p. 89)

17:55–18:20The graph-value random variable and the unique ex-istence of probabilistic measurementXianmin Geng Nanjing University of Aeronauticsand Astronautics (p. 80)

30

CT08: Levy Processes

16:25–16:50On scale functions of spectrally negative Levy pro-cesses with phase-type jumpsKazutoshi Yamazaki Osaka University (p. 96)

16:55–17:20Spectral theory for subordinate Brownian motions inhalf-lineMateusz Kwasnicki Wrocław University of Tech-nology (p. 85)

17:25–17:50The symbol of an Ito process and its relations to finepropertiesJan Alexander Schnurr Technical University Dort-mund (p. 92)

17:55–18:20Composition with distributions of Wiener-Poissonvariables and its asymptotic expansionYasushi Ishikawa Ehime University (p. 82)

CT14: Mathematical Finance and Risk Analy-sis

16:25–16:50Operational risk measure in Bayesian contextMarie Kratz ESSEC Business School (p. 84)

16:55–17:20Risk averse asymptotics in a Black-Scholes marketon a finite time horizonStefan Thonhauser University of Lausanne (p. 94)

17:25–17:50Compensators and defaultable securitiesRamin Okhrati Concordia University (p. 88)

17:55–18:20Parameter-dependent optimal stopping problemsfor one-dimensional diffusionsChristoph Baumgarten Technische UniversitatBerlin (p. 75)

CT21: Random Media

16:25–16:50Random walks in random environment with un-bounded jumps and Knudsen billiards with driftSerguei Popov University of Campinas (p. 89)

16:55–17:20On the behavior of the population density of branch-ing random walks in random environmentMakoto Nakashima Kyoto University (p. 87)

17:25–17:50Exact value of the resistance exponent for four di-mensional random walk traceDaisuke Shiraishi Kyoto University (p. 93)

17:55–18:20Brownian motion among heavy tailed PoissonianpotentialRyoki Fukushima Tokyo Institute of Technology(p. 79)

CT24: SPDE and its Applications

16:25–16:50On stochastic Burgers PDEs with random coeffi-cients and a generalization of the Cole-Hopf trans-formationNikolaos Englezos University of Piraeus (p. 78)

16:55–17:201-D quintic NLS with white noise dispersionYoshio Tsutsumi Kyoto University (p. 95)

17:25–17:50Stochastic model for second grade fluids: existence,uniqueness results and α-limitPaul Andre Razafimandimby University of Preto-ria (p. 90)

17:55–18:20On the strong solution for the stochastic 3D Leray-alpha model of turbulenceGabriel Deugoue University of Pretoria- SouthAfrica (p. 77)

31

Friday, September 10th 14:20–15:45 (Parallel sessions)


Science Hall SS01: Branching Processes and Heavy Tails (Borovkov)Room 802 SS03: Dirichlet Forms and Applications (Takeda)Life Hall SS11: Probabilistic Analysis of Algorithms (Devroye)Senri Room A SS15: Probability and Zeta Function (Matsumoto)Senri Room B SS16: Quantum Physics by Stochastic Analysis (Hiroshima)Room 502 CS03: Multifractional Processes and Fields (Ayache)Room 503 CS05: Noncolliding Diffusion Processes and Random Matrix Theory (Tanemura)Room 601 CS11: Stochastic Dynamical Systems (Doobko)Room 602 CT04: Error Estimates and MCMCRoom 604 CT05: Infinite-Dimensional Analysis for FinanceRoom 701 CT13: Mathematical Finance 4Room 801 CT17: Mathematical Statistics 3Room 603 CT22: Random Walks and Random Graphs



SS01: Branching Processes and Heavy TailsKostya Borovkov (University of Melbourne)

14:20–14:45Multidimensional branching random walk withbranching at the origin onlyVladimir Alekseevich Vatutin Steklov Mathemati-cal Institute

14:50–15:15Lower limits and equivalences for random sums ofrandom variables with heavy-tailed distributionsSergey Foss Heriot-Watt University

15:20–15:45Age and population dependent branching pro-cessesFima C Klebaner Monash University

SS03: Dirichlet Forms and ApplicationsMasayoshi Takeda (Tohoku University)

14:20–14:45Heat kernel asymptotics for the measurable Rie-mannian structure on the Sierpinski gasketNaotaka Kajino Kyoto University

14:50–15:15Some diffusion processes associated with two pa-rameter Poisson-Dirichlet distribution and DirichletprocessWei Sun Concordia University

15:20–15:45On transformation of Markov processesJiangang Ying Fudan University

SS11: Probabilistic Analysis of AlgorithmsLuc Devroye (McGill University)

14:20–14:45Infinite extensions of the Mallows model for randompermutationsAlexander Gnedin Utrecht University

14:50–15:15Variance of random digital tree structuresHsien-Kuei Hwang Institute of Statistical Science,Academia Sinica

32

15:20–15:45Clique number of high-dimensional random geomet-ric graphsGabor Lugosi Pompeu Fabra University

SS15: Probability and Zeta FunctionHiroyuki Matsumoto (Yamagata University)

14:20–14:45Zeta function and Brownian motion on matricesPhilippe Biane CNRS IGM Universite Paris-Est

14:50–15:15Random matrices and number theory: GaussianfluctuationsPaul Bourgade Harvard University

15:20–15:45On the value-distribution of log L and L’/LKohji Matsumoto Nagoya University

SS16: Quantum Physics by Stochastic Analy-sisFumio Hiroshima (Kyushu University)

14:20–14:45Quantum physics and stochastic deformationJean Claude Zambrini GFM,University Lisbon

14:50–15:15Properties of fractional Schrodinger operators byfunctional integration methodsJozsef Lorinczi Loughborough University

15:20–15:45Spectral analysis of QFT by functional integrationswith jump processesFumio Hiroshima Kyushu University

CS03: Multifractional Processes and FieldsAntoine Ayache (Laboratory Paul Painleve Uni-versity Lille 1)

14:20–14:45Linear multifractional stable motion: Wavelet meth-ods and sample paths propertiesJulien Hamonier Universite Lille1

14:50–15:15On the identification of hidden pointwise Holder ex-ponentsQidi Peng Paul Painleve laboratory, Lille 1 university

15:20–15:45LND of multiparameter mfBmAntoine Ayache Laboratory Paul Painleve, Univer-sity Lille 1

CS05: Noncolliding Diffusion Processes andRandom Matrix TheoryHideki Tanemura (Chiba University)

14:20–14:45Complex Brownian motion representation for theDyson modelHideki Tanemura Chiba University

14:50–15:15Determinantal processes and entire functionsMakoto Katori Chuo University

15:20–15:45Height fluctuations of 1D KPZ equationTomohiro Sasamoto Chiba University

CS11: Stochastic Dynamical SystemsValery Doobko (National Aviation University)

14:20–14:45Equation for kernels of integral invariants of gener-alized Ito equations and their connection with someequations of the stochastic processes theoryValery Doobko National Aviation University

14:50–15:15(blank)

15:20–15:45T.B.A.Nataly Markova

CT04: Error Estimates and MCMC

14:20–14:45New estimate of the false-positive rate of a BloomfilterAllen Roginsky National Institute of Standards andTechnology (NIST)

14:50–15:15Fault-detecting time evaluations by discretestochastic models on software fault-failure pro-cessesShuen-Lin Jeng National Cheng Kung University

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15:20–15:45Convergence of Markov measure valued randomvariables and its application to MCMCKengo Kamatani University of Tokyo

CT05: Infinite-Dimensional Analysis for Fi-nance

14:20–14:45Asymptotic expansion for a martingale with a mixednormal limit distributionNakahiro Yoshida University of Tokyo and JST

14:50–15:15Stochastic expansion for the pricing of call optionswith discrete dividendsPierre Etore LJK - ENSIMAG

15:20–15:45Infinite dimensional calculus via regularization withfinancial motivationsCristina Di Girolami University LUISS Guido Carli


14:20–14:45On the robustness of the Snell envelope applied tothe analysis of various approximation schemesPeng Hu INRIA - University Bordeaux 1

14:50–15:15The tracking error rate of the Delta-Gamma hedgingstrategyAzmi Makhlouf Osaka university

15:20–15:45Discretization error in stochastic integrationMasaaki Fukasawa Osaka University


14:20–14:45Wavelet estimation of time-varying linear systemparameters based on time-varying moving averageprocessParisa Yoosefi Zouj Islamic Azad University

14:50–15:15A re-sampling algorithm to determine best stoppingcriterion and variable selection in Cox’s proportionalhazard modelSalahuddin Kahn University of Peshawar

15:20–15:45Heuristics for recovery processesGeorge Otieno Orwa JKUAT

CT22: Random Walks and Random Graphs

14:20–14:45Extended random signal-to-interference-and-noise-ratio graphs with fadingSrikanth Krishnan Iyer Indian Institute of ScienceBangalore

14:50–15:15Realization of a finite-state mixing Markov chain asa random walk subject to a synchronized road col-oringKenji Yasutomi Ritsumeikan University

15:20–15:45Random spanning trees on the Sierpinski gasketMasato Shinoda Nara Women’s University

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Poster Session I, Tuesday and Wednesday

Scattering length for dual Markov processesPing He Shanghai University of Finance and Eco-nomics (p. 98)

The integration parts by formula of Bessel randompoint fieldRyuichi Honda Kyushu University (p. 98)

One–dimensional space–discrete transport subjectto Levy perturbationsIlya Pavlyukevich Friedrich Schiller University ofJena (p. 100)

On the Markov transition kernel for first-passagepercolation on the ladderEckhard Schlemm Technische Universitat Munchen(p. 100)

Uniform infinite Lorentzian triangulation and criticalbranching processValentin Sisko Universidade Federal Fluminense(p. 101)

Martingale approach on the expected first passagetime of uniformly EWMA procedureSaowanit Sukparungsee King Mongkut’s Univer-sity of Technology (p. 101)

Scaling relations for percolation in the high temper-ature Ising Model on the square latticeMasato Takei Osaka Electro-Communication Uni-versity (p. 101)

Asymptotics of IDS for a randomly perturbed latticeNaomasa Ueki Kyoto University (p. 102)

Basic properties of a long range perturbation of theone dimensional Kac modelMaria Eulalia Vares Centro Brasileiro de PesquisasFisicas (p. 102)

Percolation for two dimensional non-ideal gasAnatoly Yambartsev Universidade de Sao Paulo(p. 103)

Monitoring targets and variances on dependent pro-cess stepsSu-Fen Yang National Chengchi University (p. 103)

Penalisation of a stable Levy process involving itsone-sided supremumYuko Yano Kyoto University (p. 103)

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Poster Session II, Thursday and Friday

Explicit expression of average run length for expo-nential CUSUMYupaporn Areepong King Mongkut’s University ofTechnology (p. 98)

Trade-offs in pre-scheduled queueing processes.Application to air transportationClaus Peter Gwiggner Electronic Navigation Re-search Institute (p. 98)

Market information and random fieldsLane Hughston Imperial College London (p. 99)

Continuous-time random and quantum walks on thethreshold network modelYusuke Ide Kanagawa University (p. 99)

Stochastic control: with applications to portfolio op-timizationludovic Tangpi Ndounkeu African Institute forMathematical Sciences (p. 99)

College mathematical readiness of the senior highschool students in the public schools of district 1,Davao CityMelanie Joyno Orig University of Mindanao(p. 100)

Spectral measure of quantum walksEtsuo Segawa Tokyo Institute of Technology(p. 100)

Probabilistic interpretation of the forward problem ofelectrical impedance tomographyMartin Simon Johannes Gutenberg UniversitatMainz (p. 101)

Distribution of return point memory configurationsfor systems with stochastic inputsGrigory Temnov University College Cork (p. 102)

Using approximation Bayesian computation for test-ing founder effect speciation modelsPi-Wen Tsai National Taiwan Normal University(p. 102)

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Abstracts

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Plenary TalksOn the non-degenerate slowdown diffu-sion regimeRami ATAR (Technion)

I will describe diffusion limit results for criticallyloaded queueing systems, emphasizing how differentdiffusive scalings may lead to different limits, andmention one new limit process. I will also describehow controlled diffusion models help identify asymp-totically optimal control policies.

Based on joint works with Nir Solomon and ItaiGurvich.

Gradient models with non-convex inter-actionsMarek BISKUP (UCLA and University of SouthBohemia)

I will discuss recent progress in the understandingof gradient models on the hypercubic lattice wherescalar fields are coupled via a generally non-convexpotential. I will specifically highlight non-uniquenessof the Gibbs measure for a given tilt and its relationto (the lack of) strict convexity of the surface tension.I will also outline some attempts in formulating re-sults that suppose strict convexity (or even differentia-bility) of the surface tension instead of making directassumptions on the interaction. I will put these ad-vances in proper perspective with the well-establishedtheory for the case of convex interactions. The talkwill partly be based on joint papers with R. Koteckyand H. Spohn.

Spatially rough stochastic PDEsMartin HAIRER (University of Warwick)

It is a well-known fact that different interpretationsof the stochastic integral lead to genuinely differentnotions of solutions to stochastic differential equa-tions. These solutions differ by an ‘Ito-Stratonovichcorrection’, which is proportional to the cross varia-tion of the stochastic integrand and the driving Brow-nian motion. This lecture will focus on a similar phe-nomenon, which can arise due to the spatial roughnessof a class of one-dimensional stochastic PDEs.

As a prototype of the kind of equations consideredin this lecture, let u be the solution to the stochasticBurgers equation:

∂tu = ∂2xu + u∂xu + ξ ,

where ξ denotes space-time white noise. The nonlin-earity of this equation can be regularised in a naturalway by setting

Dεu(x) =u(x + aε) − u(x − bε)

(a + b)ε,

for some a, b ≥ 0 with a+b > 0. Since the solutions tothe stochastic Burgers equation have spatial regularitythat is similar to the temporal regularity of Brownianmotion, it turns out that the solutions to the regularisedequation converge to different limits, depending on thevalues of a and b. In this particular case, the ‘correct’solution can be defined by using integration by parts,and the approximations converge to that solution if andonly if a = b.

An interesting question then arises when consider-ing systems of such equations, which do appear natu-rally in the context of path sampling. Generically, thenonlinearity then cannot be written as a total deriva-tive, so that even the notion of a solution is not clear apriori since the equation does not admit a natural weakformulation anymore.

Our aim in this lecture will be twofold. First, wewill give a consistent treatment of a large class ofequations of the above type that allows to compute thecorresponding ‘Ito-Stratonovich’ correction. Second,we will show how it is possible to use rough path the-ory to give an intrinsic notion of a solution to suchequations that is canonical and does not rely on a par-ticular family of approximations.

Martingale dimensions for self-similarfractalsMasanori HINO (Kyoto University)

One approach to study the structure of stochasticprocesses is to investigate the space of martingales as-sociated with them; such kind of studies date back to1960s. The martingale dimension dm, which is also

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called the multiplicity of filtration, is interpreted as thenumber of “independent noises” that the process con-tains. Unlike the typical cases when dm coincides withthe dimension of the underlying space, for Brownianmotion on fractals, the relation between dm and otherkinds of dimensions has not been fully understood yet.In this talk, I will discuss recent progress on this sub-ject.

Discretization of processes and applica-tions to high-frequencyJean JACOD (UPMC (Paris-6))

In the context of high frequency data, like financialdata, many questions have been solved in the recentyears: for example the estimation of the volatility isby now quite well understood under very general hy-potheses, as are some questions about the presenceand some specific features of the jumps when they arepresent.

This talk will be a rather general survey of the re-cent advances on this topic, starting with an accounton some limit theorems for functionals of the incre-ments of a semimartingale. Then we will show howthese results can be used for analyzing high-frequencydata, including some empirical results on stock pricesor exchange rates. Emphasis will be put on some stillwidely open problems, like microstructure noise andirregularly or non-synchronous data.

Construction and properties of a ran-dom time with a given Azema super-martingaleMonique JEANBLANC (Mathematics Depart-ment, Evry University)

Joint work with S. SongAssuming that a supermartingale G, on a probability

space (Ω, (Ft)t≥0, P), is valued in [0, 1], we construct aprobability Q and a random times τ on the extendedspace [0,∞] × Ω such that the restriction of Q on F∞is equal to P and Q(τ > t|Ft) = Gt. We then givethe decomposition of (Ft)-martingales as (Gt) semi-martingales where (Gt) is the filtration (Ft) enlargedprogressively with τ.

On randomly-forced heat equationsDavar KHOSHNEVISAN (Department ofMathematics, The University of Utah)

The purpose of this talk is to outline some of the re-cent joint work with M. Foondun on the stochastic heatequation and its connections to ideas from renewal the-ory on one hand and optimal regularity of PDs on theother hand. The notion of “intermittency” is one of thethemes presented in this talk, and we explore its deepconnections to the potential theory of analytic semi-groups.

Convergence of symmetric Markovchains on Zd

Takashi KUMAGAI (Kyoto University)

For each n, let Y (n)t be a symmetric Markov chain

on n−1Zd. We give conditions for the weak conver-gence of the Y (n)

t to a symmetric Markov process Yt onRd. The limit process Yt can be either a diffusion, or ajump process, or a mixture of them. Discrete approx-imations of symmetric Markov processes on Rd byMarkov chains on n−1Zd will be also discussed. Theseresults generalize the work of Stroock-Zheng (1997),in which approximations of divergence forms by fi-nite range symmetric Markov chains are established.At the heart of the procedure are recent progress ofthe De Giorgi-Moser-Nash theory for jump processes.This talk is based on several joint work with my co-authors; R.F. Bass, Z.-Q. Chen, M. Kassmann, P. Kimand T. Uemura.

Metastability of Markov processesClaudio LANDIM (IMPA)

We examine the metastable behavior of a trap modelon a discrete torus and of a condensed zero range pro-cess on a finite set. The asymptotic dynamics of thefirst model is described by the K-process introducedby Fontes and Mathieu.

Geometric, fractal, and multifractalproperties of the Schramm-Loewnerevolution (SLE)Gregory F. LAWLER (University of Chicago)

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The Schramm-Loewner evolution (SLE) was in-vented by Oded Schramm as a continuum model fortwo-dimensional statistical physics “at criticality”. Itsdefinition uses the fact that such systems are expectedto exhibit conformal invariance. SLE gives a one-parameter family of curves; as the parameter variesthe fractal dimension of the curve changes. I will givean introduction to the process and then will discuss re-cent results on the fractal and multifractal nature of thecurve. One nice feature of SLE is that many interest-ing properties can be discovered using standard toolsof stochastic analysis.

Rough PathsTerence John LYONS (Wallis Professor of Math-ematics University of Oxford)

Mathematics provides many powerful tools tomodel the evolution of and interactions between sys-tems. The theory of differential equations introducedby Newton has been spectacularly successful. Morerecently Ito’s modification of this theory has allowedfor differential equations where some of the compo-nents of the system behave like Brownian motion.Ito’s extension required a new calculus.

There are many settings where systems are of highdimension and where the projection onto low dimen-sional spaces are highly oscillatory but not well mod-elled by semi-martingales and so outside the Ito calcu-lus.

The theory of Rough Paths tackles this problem.Building on tools from analysis and from algebra pro-vides new tools for describing the evolution and inter-action between systems that oscillate wildly. For ex-ample it is possible to model systems driven by frac-tional Brownian motion. The talk will introduce someof the basic concepts.

Scaling limits of random planar mapsGregory MIERMONT (Departement deMathematiques, Universite de Paris-Sud 11)

A planar map is an embedding of a graph in the2-dimensional sphere, considered up to orientation-preserving homeomorphism of the sphere. In the re-cent years, there has been a growing interest in study-ing properties of large random planar maps and theirscaling limits, with motivation coming from statistical

physics, combinatorics and probability theory. Thistalk will review some of these aspects, and describerecent results about scaling limits of random quadran-gulations or random maps with large faces.

Mathematical Finance: the P&LChris ROGERS (Statistical Laboratory, Universityof Cambridge)

Finance is one of the major application areas ofprobability, and has been for at least a quarter of acentury now. But what has the mathematical financecommunity contributed in that time? What results andideas were generated, and did anyone outside the com-munity take any notice?

The intention of this talk is to survey some of themain themes of the subject over the last couple ofdecades; to scrutinize some of the questions posed andsolved; and to assess the extent to which our work hasaffected (and been affected by) practice.

Scaling exponents for 1+1-dimensionaldirected polymersTimo O. SEPPALAINEN (University ofWisconsin-Madison)

In 1+1 dimensions directed polymers are expectedto behave superdiffusively: the order of magnitude ofthe fluctuations of the polymer path is described by theexponent 2/3, in contrast with the exponent 1/2 of dif-fusive paths such as standard random walk and Brown-ian motion. Recently this exact value of the fluctuationexponent has been proved for two particular polymermodels, a discrete model with log-gamma distributedweights and a model with a Brownian random envi-ronment. In addition, these models have a particularboundary condition which in a sense corresponds to astationary initial state. This talk describes the modelsand the ideas that lead to the results, including a Burkeproperty that gets its name from an analogy with well-known results from queueing theory.

Optimal Transportation, Gradient Flowsand Wasserstein DiffusionKarl-Theodor STURM (Institute for AppliedMathematics, University of Bonn)

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We present a brief survey on recent progress in op-timal transportation on manifolds and metric spaces.

Firstly, we will introduce the Riemannian structureon the space P(M) of probability measures induced byoptimal transports on a given Euclidean or Rieman-nian space M. And we recall the characterization ofthe heat equation on M as the gradient flow for therelative entropy on the L2-Wasserstein space P(M).Of particular interest are recent extensions to the heatflow on Finsler spaces, Heisenberg groups and Wienerspaces.

We explain how convexity properties of the rela-tive entropy on the Wasserstein space are related withfunctional inequalities (e.g. logarithmic Sobolev in-equalities), with concentration of measure and withequilibration and contraction properties of the associ-ated stochastic processes. We also sketch some recentapplications and links to Ricci flow which allow toderive or reformulate various monotonicity formulasof Perelman in terms of optimal transports or equiva-lently in terms of stochastic parallel transports.

Convexity properties of the relative entropyEnt(.|m) also play an important role in a powerful con-cept of generalized Ricci curvature bounds for metricmeasure spaces (M, d,m), introduced by Lott & Vil-lani and the author.

Finally, we present recent results for the Wasser-stein diffusion, a canonical reversible process (µt)t≥0on the Wasserstein space P(R). This includes: particleapproximation, logarithmic Sobolev inequaltiy, quasi-invariance of its invariant measure, – the so-called en-tropic measure dPβ(µ) formally given as 1

Z exp(−β ·Ent(µ|m))dP0(µ).

On Backward Stochastic Partial Differ-ential EquationsShanjian TANG (School of Mathematical Sci-ences, Fudan University, Shanghai, China)

In this talk, I shall first motivate the theoryof backward stochastic partial differential equations(BSPDEs). Then I shall recall some previous results,including the pioneering work of Alain Bensoussanand early works of Fudan Group. Following is the in-troduction of the recent new progress in the theory ofBSPDEs, made by my students and I. Finally, I shallintroduce some unsolved problems and backward dou-bly stochastic partial differential equations.

The integral geometry of random levelsetsJonathan TAYLOR (Stanford University)

In various scientific fields from astrophysics to neu-roimaging, researchers observe entire images or func-tions rather than single observations. The integralgeometric properties, notably the Euler characteris-tic of the level/excursion sets of these functions, typi-cally modelled as Gaussian random fields, have foundsome interesting applications in these domains. Inthis talk, I will describe some of the integral geomet-ric properties of these random sets, particularly theirLipschitz-Killing curvature measures. I will focus ondescribing the results, as well as providing details for aclass of non-Gaussian random fields (built up of Gaus-sians) which highlights the relation (which we referto as a Gaussian Kinematic Formula) between theirLipschitz-Killing curvature measures and the classicalKinematic Fundamental Formulae of integral geome-try.

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Ito Memorial LecturesReminiscence K. Ito. Some memoriesand some remarks on his mathematicalstyleHenry P. MCKEAN (Courant Institute of Mathe-matical Sciences)

A review on the development ofstochastic analysisShinzo WATANABE (Kyoto University)

In this memorial lecture, I will review on the devel-opment of stochastic analysis in these nearly eighty orninety years, referring much to my personal memoriesof Professor Kiyosi Ito.

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Invited Special SessionsCOH formula and Dirichlet Laplacianson small domains of pinned path spacesShigeki AIDA (Tohoku University)

We consider a small domain of a pinned path spaceover a compact Riemannian manifold. We establish aClark-Ocone-Haussman formula for functions whichbelong to H1-Sobolev space on the domain with theDirichlet boundary condition and apply it to obtainspectral gap estimate for the Dirichlet Laplacians.

Heat and Weyl asymptotics for stableprocessesRodrigo BANUELOS (Purdue University)

After recalling some of the well known results onthe heat and Weyl asymptotics for the classical Lapla-cian (Brownian motion), we will address similar ques-tions for the fractional and relativistic Laplacian (sta-ble processes and relativistic stable processes).

The self-dual point of the two-dimensional random-cluster model iscritical for q ≥ 1Vincent BEFFARA (UMPA - ENS Lyon)

We prove a long-standing conjecture on random-cluster models, namely that the critical point for suchmodels with parameter q ≥ 1 on the square lattice isequal to the self-dual point psd(q) =

√q/(1 +

√q).

This gives a proof that the critical temperature of theq-state Potts model is equal to log(1+

√q) for all q ≥ 2.

We further prove that the transition is sharp, meaningthat there is exponential decay of correlations in thesub-critical phase. The techniques of this paper arerigorous and valid for all q ≥ 1, in contrast to earliermethods valid only for certain given q.

This is joint work with Hugo Duminil-Copin(Geneva); reference arXiv:1006.5073.

On fractional Levy processesChristian BENDER (Saarland University)

A statistical analysis of many real world phenomenain such diverse fields as finance, econometrics, hydrol-ogy, or internet traffic, reveals long memory effects.

Arguably, among the best-studied stochastic processeswith long range dependence are fractional Brownianmotions (with Hurst parameter H > 1/2). FractionalLevy processes are generalizations of fractional Brow-nian motions which capture the memory effects in asimilar fashion but provide more flexibility concerningthe modeling of the distribution. They can be definedby replacing the driving Brownian motion in an inte-gral representation of a fractional Brownian motion bymore general Levy processes.

In this talk we characterize the semimartingaleproperty of a fractional Levy process by various equiv-alent conditions, one of which is in terms of the char-acteristic triplet of the driving Levy process, while oth-ers are in terms of differentiability properties of thesample paths. Motivated by the fact that fractionalLevy processes may fail to be semimartingales, we in-troduce a stochastic calculus in the Skorokhod sensefor fractional Levy processes and related processeswhich can be obtained by convolution of a determinis-tic kernel with a Levy process.

This is based on joint work with A. Lindner, T. Mar-quardt, and M. Schicks.

Zeta function and Brownian motion onmatricesPhilippe BIANE (CNRS, IGM, Universite Paris-Est)

We consider Brownian motion on several spaces ofmatrices, and their associated Laplacian. To such aLaplacian is associated a random varaible, via gener-alized gamma convolution. In the case of S U(2) itsMellin transform is the Riemann completed zeta func-tion. In the case of S L(2,C)/S U(2) the Mellin trans-form is a function considered by Polya, which satisfiesRiemann hypothesis.

Computing likelihoods under multiple-merger coalescentsMatthias BIRKNER (University Mainz)

In population genetic scenarios with extremely highvariability in individual offspring numbers, more gen-eral coalescents than Kingman’s coalescent can appear

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as the genealogy connecting a sample. We present andcompare various importance sampling methods whichallow to compute likelihoods using sequence data inthe context of multiple merger coalescents, generalis-ing results of Griffiths and Tavare, Stephens and Don-nelly and Hobolth, Uyenoyama and Wiuf. We illus-trate these methods using simulated and some realdatasets.

Based on joint work with Matthias Steinrucken(Berkeley) and Jochen Blath (TU Berlin).

The Symbiotic Branching Model: Mo-ment Spectrum, Longtime-behaviourand Width of the InterfaceJochen BLATH (TU Berlin)

In this talk we discuss some of the longterm- andpath-properties of the so-called ’symbiotic branchingmodel’, introduced by Etheridge and Fleischmann in2004. The model can be viewed as a spatial system oftwo interacting species who can only reproduce if bothtypes are simultaneously present in the same location.Parametrised by a correlation parameter ρ, the modelprovides a unified framework for several classical par-ticle systems, like the stepping-stone and a (versionof) the parabolic Anderson model. We show that itexhibits a rich and interesting longterm behaviour andprove a result about the propagation of its interface. Akey to the understanding of this model lies in an ex-plicit ’moment spectrum’ given as a function of ρ.

The talk is based on a joint paper with Leif Doering(Berlin) and Alison Etheridge (Oxford), to appear inthe Annals of Probability (2010).

Phase transition in kinetically con-strained modelsThierry BODINEAU (Ecole NormaleSuperieure)

We will discuss the large deviations of the activityin kinetically constrained models. A first order phasetransition occurs in these models due to the constraintsin the dynamics. We will show that the finite sizescaling of this first order dynamical phase transitionis reminiscent of the transition occurring in the Isingmodel.

Stochastic differential equations withboundary noiseStefano BONACCORSI (University of Trento,Department of Mathematics)

We discuss some possible examples and applica-tions of stochastic evolution equations with boundarynoise.

No asymptotic arbitrage in models withtransaction costs and production ca-pacitiesBruno BOUCHARD (CEREMADE, UniversityParis-Dauphine CREST, ENSAE)

As in Bouchard and Pham (2005), we consider ageneral discrete time model with proportional trans-action costs and production capacities. Contrary tothe above paper, the level of production on the period[t, t + 1] does not only depend on the time-t level ofinventories but is fully controlled by a Rd-valued con-trol process β. Its impact on the wealth process at timet in −βt, which means that some goods are used forthe production process. At time t + 1, it increases thewealth process by Rt+1(βt), which typically means thatthe production is sold and therefore increases the com-ponent of the wealth process corresponding to curren-cies. The random map Rt+1 is only known at time t+1.

In this context, we study the notion of no-asymptotic arbitrage. Namely, we allow for small ar-bitrages due to production but assume that there existsa linear map β 7→ ct+1 + Lt+1β satisfying Rt+1(βt) ≤ct+1 + Lt+1β and such that the linear model in which Ris replaced by β 7→ +Lβ does not have arbitrage op-portunities.

In the context of the linear model, we introduceto extended notions of robust no-arbitrage and no-arbitrage of second kind, and show that there areequivalent to the existence of a corresponding notionof strictly consistent price system.

This allows to show that the set of terminal wealthis closed in the original non-linear model. As usual,this leads to the formulation of a super-hedging theo-rem and to existence in expected utility maximisationproblems.

Examples of application in optimal power-plantmanagement are discussed.

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Random matrices and number theory:Gaussian fluctuationsPaul BOURGADE (Harvard University)

For large unitary matrices, the number of eigenval-ues in distinct shrinking intervals satisfies a centrallimit theorem, whose covariance structure is relatedto some branching processes. In this talk, we presentthese well-known random matrix results and explainthe strict analogue for the zeros of L-functions. Forlinear statistics of smooth functions of the eigenangles,the weak convergence to a normal law still holds, butwith no normalization. We will also discuss the ana-logue of this asymptotic normality in the context ofanalytic number theory.

The critical Z-invariant Ising model viadimersCedric BOUTILLIER (UPMC Paris 6 – EcoleNormale Superieure)

The Ising model is a mathematical model for ferro-magnetism where spins sit on vertices of a graph. Fora large class of two-dimensional graphs, local weightsfor configurations can be chosen to satisfy some inte-grability conditions: the model is then said to be Z-invariant.

In a joint work with Beatrice de Tiliere, we studythe Z-invariant Ising model on infinite planar graphsat the critical point. Our main tool is Fisher’s corre-spondence between the Ising model on a surface graphG and the dimer model on a decorated version of G.Using dimer techniques, we show that several prob-abilistic quantities have a closed expression that de-pends only on the local geometry of the graph.

Applications of excursion theory to con-struction and uniqueness of stochasticprocessesKrzysztof BURDZY (University of Washington)

I will outline two applications of excursion theory.The first project was concerned with the stationary dis-tribution for Brownian motion with inert drift (col-laborators: R. Bass, Z. Chen and M. Hairer). Thesecond project was concerned with non-extinction ofFleming-Viot type branching particle system (collabo-rators: M. Bieniek and S. Finch).

Estimates on the Boltzmann collisionkernel via analysis of a many particlestochastic modelEric A CARLEN (Rutgers University)

Kinetic theory, both classical and quantum, de-scribes the evolution of dilute gas of particles inter-acting through binary collisions. The equations of ki-netic theory are non-linear evolutions equations for aprobability density, or, in the quantum case, a densitymatrix. In 1956, Mark Kac proposed a strategy forinvestigating such equations via a direct analysis of astochastic model, different from and simpler than theunderlying physical collision model, but still leadingto the same equations. There has been much recentprogress, and new results in kinetic theory are now be-ing deduced by this means. This talk will present sev-eral such results, both for the classical and quantumcases.

Evolving communities with individualpreferencesThomas CASS (University of Oxford)

We consider a community of interacting individu-als, each individual having preferences described bysome probability measure on rough paths. For cer-tain types of interaction we consider the problem ofexistence and uniqueness of some forward evolution,which accounts for the individuals preference, and cor-rectly models the interaction with the aggregate be-haviour of the community. The evolution of the popu-lation need not be governed by any over-arching PDE,but in the case where it is one can match the stan-dard non-linear parabolic PDEs of McKean-Vlasovtype with specific examples of communities. Roughpaths continuity statements allows for straight forwardanalysis of propagation of chaos phenomena and largedeviations. This is joint work with Terry Lyons.

Dirichlet heat kernel estimates for frac-tional Laplacian perturbed by gradientoperatorZhen-Qing CHEN (University of Washington)

Suppose d ≥ 2 and α ∈ (1, 2). Let D be a boundedC1,1-open set in Rd and b an Rd-valued function on

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D whose components are in certain Kato class of theisotropically symmetric α-stable process. In this talk,I will present sharp two-sided heat kernel estimates for∆α/2 + b · ∇ in D with zero exterior condition.

This is a joint work with P. Kim and R. Song.

Higher order freeness and asymptoticrepresentations of unitary groupsBenoit VP COLLINS (University of Ottawa)

It has been proved by Biane that operations on‘large’ representations of the unitary group exhibiteda behaviour similar to that of random matrices, in thesense that this behaviour was governed by asymptoticfreeness. In the asymptotic study of large dimensionalunitarily invariant random matrices, results beyondasymptotic freeness have been established - e.g. thestudy of fluctuations of moments and sums of randommatrices. This refined study is governed by a conceptof ‘higher order freeness’. In this talk, we will showthat the fluctuations of large representations of the uni-tary group are also governed by higher order freenessunder fairly general assumptions. This is joint workwith Piotr Sniady.

An application of the Kusuoka-Lyons-Victoir cubature method to the numeri-cal solution of semilinear PDEsDan CRISAN (Imperial College London)

We propose a new method for the numerical solu-tion of a class of semilinear PDEs. The key propertyused here is that the solution of a PDE belonging tothis class can be written as an integral of a certain non-linear functional against the law of a diffusion. Thealgorithm involves the discretisation of the functionaltogether with an approximation of the law of the dif-fusion by using the Kusuoka-Lyons-Victoir cubaturemethod. The main results concerning upper boundsfor the error are reported and a numerical example isincluded.

This is joint work with Konstantinos Manolarakis.

Invariant random graphs with pre-scribed iid degreesMaria DEIJFEN (Department of Mathematics,Stockholm University)

Models for generating random graphs with pre-scribed degree distribution have been extensively stud-ied the last few years. Most existing models for thispurpose however do not take spatial aspects into ac-count, that is, there is no metric defined on the ver-tex set. I will discuss spatial versions of the problem.More precisely, given a degree distribution F and aspatial vertex set – for instance Zd or the points of aspatial Poisson process – how should one go aboutto obtain a translation invariant random graph on thegiven vertex set with degree distribution F? Whichproperties do the resulting configurations have? I willdescribe some existing results and a number of openproblems.

Synchrony-breaking and Rare Events inStochastic Neuronal NetworksLee DEVILLE (Department of Mathematics, Uni-versity of Illinois)

We consider a family of models for a network ofpulse-coupled oscillators containing randomness bothin input and in network architecture. We analyze thescalings which arise in certain limits, discuss the criti-cal behavior of the system in these limits, and interpretvarious “finite-size” effects as perturbations of theselimits.

Most notably, for certain parameters, this networksupports both synchronous and asynchronous modesof behavior and will switch between these modes atrandom times due to rare events. We also relate theanalysis of this network to classical results in graphtheory, and in particular, those involving the size of the“giant component” in the Erdos-Renyi random graph.

Effective Velocity for interfaces in a ran-dom environmentNicolas P DIRR (University of Bath)

We consider the so-called Random Obstacle Model:An interface is driven through a field of random obsta-cles, where the evolution law is such that a competitionbetween the desire to keep the interface ”flat” (gradi-ent flow of area) and the effect of the obstacles occurs.We present results on the resulting effective velocityon large scales.

48

Optimal stopping of piecewise deter-ministic Markov processesFrancois DUFOUR (INRIA Bordeaux Sud-Ouest)

We propose a numerical method to approximate thevalue function for the optimal stopping problem of apiecewise deterministic Markov process (PDMP). Ourapproach is based on quantization of the post jumplocation – inter-arrival time Markov chain naturallyembedded in the PDMP, and path-adapted time dis-cretization grids. It allows us to derive bounds forthe convergence rate of the algorithm and to providea computable ε-optimal stopping time. The talk is il-lustrated by a numerical example.

Unlimited liabilities, reserve capital re-quirements and the taxpayer put optionErnst Wilhelm EBERLEIN (University ofFreiburg)

When firms access unbounded liability exposuresand are granted limited liability, then an all equity firmholds a call option, whereby it receives a free option toput losses back to the taxpayer. We call this option thetaxpayer put. We value this option and determine thelevel for reserve capital. The challenge is to model therisky asset and liability processes appropriately andto extract the corresponding parameters from marketdata.

Assets excluding cash plus short term investmentsand liabilities less debt are modeled as exponentialsof two Levy processes. The two Levy processes aremodeled as linear mixtures of four independent Levyfactors. Two of these factors drive assets and liabil-ities with positive correlations while two of them in-duce negative correlations. Equity is then a call op-tion on the spread of assets over liabilities. We em-ploy recently developed methods by Hurd and Zhou(2009) to value these spread options using a two di-mensional Fourier inversion. The reserve capital re-quired by the taxpayer is determined by making theaggregate risk acceptable to the general external econ-omy at stress level 0.75 for the distortion minmaxvar.The compound spread option model is calibrated toequity option data at market close on year end to iden-tify the joint law of risky assets and liabilities. This isjoint work with Dilip Madan.

Asymptotics of characters and largeYoung diagramsValentin FERAY (LaBRI, CNRS, UniversiteBordeaux 1)

We consider the irreducible representations of thesymmetric group, which are known to be parametrizedby Young diagrams. A natural question in asymptoticrepresentation theory is the following: how does thecharacter value on a fixed permutation behave whenthe size of the diagram grows to infinity? We presentsome known results on this question (Kerov and Ver-shik 81, Biane 98).

These results can be used in a classical problemin probability: what is the shape of a large randomYoung diagrams under Plancherel’s measure. We ex-plain ideas of Kerov developed to solve this questionand show how its tools can be adapted to handle thecase of a recent deformation of the Plancherel’s mea-sure.

Shift-monotonicity and Infinite Divisibil-ity for Regenerative SetsPatrick Joseph FITZSIMMONS (Departmentof Mathematics, University of California San Diego)

A regenerative set M is the set of times when astrong Markov process visits one fixed state. The as-sociated potential measure has distribution functionU(t) = E[L(t)], where L is local time for M. We linkthe existence of a monotone density for U to stochas-tic monotonicity of M shifted by t > 0: M(t) :=(M − t) ∩ [0,∞). This notion is brought to bear on theproblem of infinite divisibility (for the operation of in-tersection) of regenerative sets. Several longstandingopen problems will be discussed.

Lower limits and equivalences for ran-dom sums of random variables withheavy-tailed distributionsSergey FOSS (School of MACS, Heriot-Watt Uni-versity)

I will give an overview of recent results on thetail asymptotics for sums for random variables havingheavy-tailed distributions. I will start with the case ofi.i.d. increments and consider various scenarios for thedistribution of their number (light or heavy) and on thedependence between the summands and their number.

49

Then I consider a model of a random sum with depen-dent increments. In all cases, I formulate conditionsfor the ”principle of a single big jump” to hold: themost likely way for the sum to be large is that one ofthe summands takes a large value.

The talk is based on joint papers with D Denisov, DKorshunov, A Richards, and S Zachary

A new pathwise theory of SPDEsPeter Karl FRIZ (TU and WIAS Berlin)

We propose the marriage of rough path analysiswith (2nd order) viscosity theory. This allows to han-dle large classes of linear- and non-linear stochasticpartial differential equations with rough path methods.Joint work with M. Caruana and H. Oberhauser.

Concentration of measure phenomenonand eigenvalues of LaplacianKei FUNANO (Kumamoto university)

In this talk, we discuss the relation between theLevy-Milman concentration of measure phenomenonand (behavior of) eigenvalues of Laplacian on a closedRiemannian manifold. This talk is based on joint workwith Takashi Shioya (Tohoku university).

Interpolation method and scaling limitsin sparse random graphsDavid GAMARNIK (MIT)

Recently a powerful approach was developed inthe physics of spin glasses based on the interpo-lation idea. Among other things, the interpolationmethod was used to prove the existence of the so-called free energy thermodynamic limits for severalspin glass models, including Sherrington-Kirkpatrick,Viana-Bray and random K-SAT models.

We propose a simple combinatorial approach to theinterpolation method and demonstrate it’s applicabil-ity in context of combinatorial optimization problemson sparse Erdos-Renyi and random regular graphs.Specifically we establish the existence of scaling lim-its for maximum independent sets, MAX-CUT, color-ing and K-SAT problems. For these models, we showthat the optimal values appropriately normalized, con-verge to a limit with high probability (w.h.p.), as thesize of the underlying graph diverges to infinity. In the

context of independent set model this resolves an openproblem posed by Aldous in 2000. Our simpler com-binatorial approach allows us to work with the zerotemperature case (optimization) directly, which sim-plifies the analysis substantially. Additionally, usingour approach, we establish the large deviations prin-ciple for the satisfiability property for constraint sat-isfaction problems such as coloring, K-SAT. The talkwill be completely self-contained. No background onrandom graph theory/statistical physics is necessary.

Joint work with Mohsen Bayati (Stanford) andPrasad Tetali (Georgia Tech).

Collective phenomena on random net-worksCristian GIARDINA (Modena and ReggioEmilia Univerisity)

The topological properties of empirical networkshave been deeply investigated. In particular, in manyreal-world networks such as the Internet, social net-works and biological networks, power-law degree se-quences have been observed. This means that, whenthe graph is large, the proportion of vertices with de-gree k is asymptotically proportional to k−a, for somea > 1. Often, these networks have a degree distribu-tion with finite mean, but infinite variance (2 < a < 3).

We will discuss the emerging properties of stochas-tic processes taking place on such random structures.We will focus on ferromagnetic Ising models on ran-dom graphs with a power-law degree distribution. Nonrigorous work by physicists predicts a universal be-havior of smooth thermodynamic quantities, indepen-dently of the degree distribution exponent. A recentwork by Dembo and Montanari [1] rigorously provesthis prediction assuming a finite variance degree dis-tribution. We show that the free energy has the univer-sal form predicted by the cavity method, in all caseswhere the random graph has a local approximation toa uniform random tree, including the case of infinitevariance degree distribution, which is found in empir-ical networks. If times permits we will also discussthe critical behavior: around the critical temperaturedifferent universality classes appear depending on thepower law exponent.

This is joint work with Sander Dommers andRemco van der Hofstad [2].

50

[1] A. Dembo, A. Montanari, Ising models onlocally tree-like graphs, The Annals of AppliedProbability 20, no.2, 565–592 (2010).

[2] S. Dommers, C. Giardina, R. van der Hofstad,Ising models on power-law random graphs,arXiv:1005.4556v1[math.PR]

Infinite extensions of the Mallows modelfor random permutationsAlexander GNEDIN (Utrecht University)

A randomised bubble sorting of a list with n dis-tinct elements iterates the following operation. Twoadjacent positions are chosen at random, then the en-tries are arranged in increasing (decreasing) order withprobability p > 1/2 (respectively, 1− p). The long-runoutcome is the Mallows distribution, which assigns topermutation σ a mass proportional to qinv(σ), whereinv(σ) counts the inversions, and q = 1/p − 1.

We are interested in properties of the Mallows per-mutation of n integers for large n, in particular inthe limit distribution of displacements σ( j) − j. Forbounded j or n − j the question can be interpretedin terms of the analog of Mallows measure on the setof permutations of N (one-sided extension), otherwisethe relevant measure is supported by certain permuta-tions of Z (two-sided extension). The extensions them-selve appear as stationary measures for a reversiblecontinuous-time Markov process. A distinguished fea-ture of the two-sided extension is the invariance of thelaw of σ( j)− j, j ∈ Z under shifts. We employ quasi-invariance of the measures under transpositions andtheir recursive construction from iid geometric vari-ables.

Joint work with Grigori Olshanski.

A Coalescent Dual Process in a Can-nings model with Genic Selection, andthe Lambda Coalescent limitRobert CharlesGRIFFITHS (University of Ox-ford)

A coalescent dual process can be derived for a classof continuous-time Cannings models with viability se-lection. In these models, individuals may give birth tomultiple offspring whose survival depends on both theparental genotype and the brood size. In the limit ofinfinite population size the non-neutral Cannings mod-els converge to a Lambda-Fleming-Viot process. The

dual is a branching-coalescing process which followsthe typed ancestry of genes backwards in time withreal and virtual lineages. This is joint research withAlison Etheridge and Jay Taylor.

Lyapunov conditions for functional in-equalitiesArnaud GUILLIN (Laboratoire de Mathema-tiques Universite Blaise Pascal)

We will show how a simple approach based onLyapunov conditions enables to prove various func-tional inequalities (Poincare, logarithmic Sobolev,weak Poincare, transportation). We find back usualknown conditions and often generalize them.

Accelerated numerical schemes for de-terministic and stochastic PDEsIstvan GYONGY (University of Edinburgh)

A class of numerical schemes for linear determinis-tic and stochastic PDEs is considered and the rate ofconvergence of numerical solutions is investigated. Itis shown that the order of accuracy of the schemes canbe made as high as wanted by an implementation ofRichardson’s method. The talk is based on recent jointresults with Nicolai Krylov.

Robust Utility Maximization for LevyMarket ModelsDaniel HERNANDEZ (Centro de Investigacionen Matematicas)

In this talk we consider a robust version of theportfolio optimization problem, in which asset pricesare represented by the Doleans-Dade exponential of aLevy process. Sufficient conditions to obtain the dualrepresentation are given, which has the form of a min-min problem on the suitable set of density measures.The parametrization of the problem in terms of densi-ties gives rise to a stochastic control problem in thoseprocesses. This problem is studied using dynamic pro-gramming arguments. Also, the connection with riskmeasures is explored. This is a joint work with LeonelPerez-Hernandez

51

Modelization of membrane potential andinformation transmission in large sys-tems of neuronsReinhard HOEPFNER (University of Mainz)

In a first part of the talk, we present a stochasticmodel for information transmission in large systemsof neurons. Here the membrane potential in the sin-gle neuron is modelled as a Cox-Ingersoll-Ross typejump diffusion with explicit time dependence in thedrift, and spike generation as conditionally Poisson.We give a limit theorem which shows how a large sys-tem of neurons processing the same signal can trans-mit this signal up to some small deformation of itsshape.

In a second part of the talk, we consider sets of datawhere the membrane potential in a pyramidal neu-ron (belonging to a cortical slice observed in vitro)is recorded under different experimental conditions.First, assuming that the membrane potential betweensuccessive spikes can be modelled as a time homoge-neous diffusion process, nonparametric estimates fordiffusion coefficient and drift make appear three rel-evant classes of diffusion models. Second, consider-ing p-variations (p=2 and p=4) and relying on recentresults of Ait-Sahalia and Jacod (2009), we ask thequestion to which extent a (continuous) semimartin-gale model is in fact adaequate for the membrane po-tential between successive spikes: in our data, a sur-prising difference appears –in the same neuron– be-tween spiking and non-spiking regimes.

Variance of random digital tree struc-turesHsien-Kuei HWANG (Institute of Statistical Sci-ence, Academia Sinica)

Random digital tree structures are simple and use-ful prototype data structures whose asymptotic vari-ances are often very difficult to compute. A systematicapproach is proposed to facilitate such calculationsand many new results are presented; also new iden-tities for the variances are given, which are themselvesasymptotic expansions in nature. The tools we de-velop apply to tries, digital search trees, Paticia trees,bucket sort, communication protocols, etc. (This talkis based on joint work with Michael Fuchs and VytasZacharovas.)

Laplace-type asymptotics for rough dif-ferential equation driven by fractionalBrownian motionYuzuru INAHAMA (Nagoya University)

In this talk we discuss Laplace-type asymptotic the-orem for ”small noise limit” of rough differential equa-tions driven by fractional Brownian motion with Hurstparameter between 1/4 and 1/2. This type of problemshas a long history. It was initiated by Azencott in 1982for SDEs in the usual sense which is driven finite di-mensional Brownian motion. The key of the proof isthe Taylor expansion of the Ito map in the rough sensearound the point, at which the minimum is achieved.

Dissipative Abelian sandpiles and rateof convergenceAntal A JARAI (University of Bath)

In the standard Abelian sandpile model defined ona finite Λ ⊂ Zd, chips are only lost at the boundaryof Λ. In dissipative sandpiles, chips can be lost at ev-ery site of Λ. We study a continuous height version ofthe Abelian sandpile on Zd, that allows arbitrary smallamount of dissipation in the bulk. We show that cor-relations decay exponentially, and likewise the proba-bility that x is involved in an avalanche initiated at 0.In the limit as the dissipation goes to 0, the standardsandpile is recovered. In dimensions d = 2, 3, we giveestimates on the rate of convergence at the level of thestationary measures.

Heat kernel asymptotics for the measur-able Riemannian structure on the Sier-pinski gasketNaotaka KAJINO (Graduate School of Informat-ics, Kyoto University)

On the Sierpinski gasket K, Kigami [3] has intro-duced the notion of the ‘measurable Riemannian struc-ture’ which is obtained by regarding K as a ‘Rieman-nian submanifold in R2’ through a harmonic embed-ding (an injective harmonic map) Φ : K → R2. Thenthe image KH := Φ(K), called the harmonic Sierpinskigasket (see [2, Figure 1.2] for its picture), can be con-sidered as the geometric realization of the Riemannianstructure, and there we have the analogues of the basicobjects in Riemannian geometry like the gradient vec-tor field ∇u of a function u, the Riemannian volume

52

measure µ and the geodesic metric dH . Moreover, by[3, Theorem 6.3], the associated heat kernel pHt (x, y)is subject to the two-sided Gaussian bound

pHt (x, y) c1

µ(B√t(x, dH )

) exp(−dH (x, y)2

c2t

)(1)

in spite of the fractal nature of the space, whereBr(x, dH ) := y ∈ K | dH (x, y) < r.

In this talk I will present various detailed short timeasymptotic behaviors of this heat kernel, which havebeen established in a recent preprint [2]. The main re-sults include:

• Varadhan’s asymptotic relation: for x, y ∈ K,

limt↓0

2t log pHt (x, y) = −dH (x, y)2. (2)

• If x is a junction point (i.e. a vertex at some level),there exists an explicit constant ξx > 0 such that

limr↓0

µ(Br(x, dH ))r

= 2ξx, (3)

and

pHt (x, y)− 1

ξx√

2πtexp

(−hx(y)2

2t

)is ‘small’ (4)

as long as y is close to x and t > 0 is sufficientlysmall, where hx denotes the coordinate along the‘tangent line of KH at x’ such that hx(x) = 0.

• Asymptotics of moments of displacement of thecorresponding diffusion X = (Xtt≥0, Pxx∈K):for any junction point x and α ∈ (−1,∞),

limt↓0

Ex[dH (x, Xt)α]tα/2

=

∫R

|y|α e−y2/2

√2π

dy. (5)

• Existence of local spectral dimension µ-a.e.:there exists dloc

S ∈ (1, 1.52) such that

limt↓0

2 log pHt (x, x)− log t

= dlocS µ-a.e. x ∈ K. (6)

• Existence and geometric characterizations of thespectral dimension: for the eigenvalues λHn n∈N

of the associated Laplacian and s, t > 0, we de-fine NH (s) := #n ∈ N | λHn ≤ s and ZH (t) :=∑

n∈N e−λHn t =

∫K pHt (x, x)dµ(x). Then

lims→∞

2 logNH (s)log s

= limt↓0

2 logZH (t)− log t

(7)

= dimH(K, dH ) = dimB(K, dH ) ∈ [dlocS , 1.52),

where dimH and dimB denote respectively Haus-dorff and box-counting dimensions.

(2), (3), (4) and (5) are ‘manifold-like’; the asymp-totic behavior of the same form as (2) is well-knownfor the heat kernels on Riemannian manifolds, and (3),(4) and (5) reflect the intuition that, around a junctionpoint x, KH looks very much like its tangent line atx. On the other hand, according to (6) and (7), pHtexhibits non-integer dimensional behaviors at µ-a.e.point, thereby reflecting the fractal nature of the space.

The proofs of (2), (3), (4) and (5) make full useof the following fact due to [1]: let h be a functionon K harmonic outside the ‘boundary’ of the gasket,and let µ〈h〉 := |∇u|2 · µ be the energy measure of h.Then the time change by µ〈h〉 of the R-valued processh(X) = h(Xt)t≥0 is a reflecting Brownian motion.[1] N. Kajino, Time changes of local Dirichlet spaces

by energy measures of harmonic functions, toappear in Forum Math.

[2] N. Kajino, Heat kernel asymptotics for themeasurable Riemannian structure on the Sierpinskigasket, preprint, 2010.

[3] J. Kigami, Measurable Riemannian geometry onthe Sierpinski gasket: the Kusuoka measure andthe Gaussian heat kernel estimate, Math. Ann. 340(2008), 781–804.

Gaussian free field and conformal fieldtheoryNam-Gyu KANG (Department of MathematicalSciences, Seoul National University)

Conformal field theory has been used to derive sev-eral exact results for the conformally invariant crit-ical clusters in theoretical physics. After a briefmathematical overview of Ward’s identities (in termsof Lie derivatives) and the related concept of thestress-energy tensor in conformal field theory, I willpresent relations between conformal field theory and

53

Schramm–Loewner evolutions. This is joint work withNikolai Makarov.

Evolution in a spatial continuumJerome KELLEHER (University of Edinburgh)

In the classical models of diffusive gene flow, indi-viduals reproduce and disperse independently. Thesemodels fail in at least three ways: large scale pat-terns cannot be explained; observed genetic diversityis much lower than predicted; and loosely linked locievolve independently. We discuss a recent model de-signed to deal with these problems. In this model,recurrent extinction events kill some fraction of thepopulation in a region, and the region is then repopu-lated by the offspring of some small number of parentsdrawn from nearby. We show how this model leads toa well defined coalescent process and discuss a relatedequation to calculate the probability of identity in statefor genes separated by a given distance.

Age and Population Dependent Branch-ing ProcessesFima C KLEBANER (Monash University)

We describe a branching model in which particleslive for a random time and upon death leave a numberof offspring. Both, the lifespan distribution as well asoffspring distribution depend on the population com-position (population-dependent Bellmann-Harris pro-cess). A special case considered is when the reproduc-tion changes between subcritical and supercritical de-pending whether the population size is below or abovea certain threshold K. We show that under reasonableassumptions such population stays around level K foran exponentially long time. Although the populationsize in such processes is not Markov, the process ofages is. Therefore we analyze the process by usinga measure-valued approach, obtaining a fluid approx-imation by a dynamical system, and a bound for theexit time from a domain of attraction of a stable pointof a dynamical system with noise. This is a joint workwith Peter Jagers, Gothenburg, Sweden.

Robust utility maximization on an infi-nite time horizonThomas KNISPEL (Leibniz University HannoverInstitute of Probability and Statistics)

We consider a stochastic factor model that accountsfor model ambiguity. For HARA utility functionswe maximize the long term growth rate of robust ex-pected utility. Using duality methods the problem isreformulated as an infinite time horizon, risk-sensitivecontrol problem. Our results characterize the opti-mal growth rate, an optimal long term trading strat-egy, and an asymptotic worst-case model in terms ofan ergodic Bellman equation. The asymptotic anal-ysis provides useful insight for investors with longbut finite time horizon. To illustrate the general re-sults, we present two explicit case studies: a geomet-ric Ornstein-Uhlenbeck model with uncertain rate ofmean reversion and a Black-Scholes model with un-certain drift terms.

[1] T. Knispel: Asymptotics of Robust UtilityMaximization, submitted.

[2] W.H. Fleming and S.-J. Sheu. Optimal long termgrowth rate of expected utility of wealth. Ann.Appl. Probab., 9(3):87-903, 1999.

A rate of convergence for loop-erasedrandom walk to SLE(2)Michael KOZDRON (University of Regina)

Among the open problems for SLE suggested byOded Schramm in his 2006 ICM talk [1] is that ofobtaining reasonable estimates for the speed of con-vergence of the discrete processes which are knownto converge to SLE. In this talk we derive a rate forthe convergence of the Loewner driving function forloop-erased random walk to Brownian motion withspeed 2 on the unit circle, the Loewner driving func-tion for radial SLE(2). This talk is based on joint workwith Christian Benes (CUNY) and Fredrik JohanssonViklund (KTH).

[1] O. Schramm. Conformally invariant scalinglimits: an overview and a collection of problems.In M. Sanz-Sole, J. Soria, J. L. Varona,and J. Verdera, editors, Proceedings of theInternational Congress of Mathematicians,Madrid, Spain, 2006. Volume I, pages 513–543. European Mathematical Society, Zurich,Switzerland, 2007.

54

Limit of characteristic polynomials of arandom matrixManjunath KRISHNAPUR (Indian Institute ofScience)

We show that the characteristic polynomials of n xn Gaussian matrices, appropriately normalized, con-verges to a random analytic function. The limit ran-dom analytic function turns out to be a Gaussian an-alytic function with respect to a random covariancekernel. We show this by proving a version of Polya’surn scheme for Hilbert space valued random variables.This is joint work with Balint Virag.

On the Goodness of Fit Tests for Er-godic Diffusion ProcessesYury A. KUTOYANTS (University of Maine)

We consider the problem of Goodness of Fit test-ing for continuous time observations of ergodic diffu-sion processes. We propose several simple tests (basedon the structure of observations) which are asymptot-ically distribution-free and are consistent against anyfixed alternative. Then we describe the Cramer-vonMises type tests constructed with the help of empiricaldistribution function and empirical density. We showthat the special choice of weight functions allows us tomake these tests asymptotically distribution free. Wediscuss the behavior of similar tests in the case of com-posite (parametric) hypothesis and the possibility ofthe construction of asymptotically optimal tests.

Random pinning model: the issue ofdisorder relevanceHubert LACOIN (Universita di Roma Tre)

Pinning model are used to describe numerous phys-ical phenomena, including interaction between an in-homogeneous polymer chain and and an attractiveinterface. It is known that at low temperature, thepolymer sticks to the interface (polymer is localized),whereas at high temperature it moves away for it. Forthe homogeneous model the caracteristic of the phasetransition are exactly known. For the inhomogeneousmodel, the main question, wether or not the featuresof the phase transition are modified by the presence ofdisorder. We’ll introduce in this talk some pieces ofanswer to this question. (based on joint work with B.Derrida, G. Giacomin, F.L. Toninelli).

Comparison geometry of the Bakry-Emery Ricci curvature on complete Rie-mannian manifoldsXiangdong LI (Academy of Mathematics and Sys-tem Science, Chinese Academy of Sciences)

Comparison theorems in Riemannian geometryhave many important applications in geometric anal-ysis. In recent years, the Bakry-Emery Ricci curvaturehas been used to establish some geometric comparisontheorems on complete Riemannian manifolds. In thistalk, we will present some important results along thisdirection.

Distributional properties of station-ary solutions of some generalisedOrnstein–Uhlenbeck processesAlexanderM. LINDNER (TU Braunschweig)

A stochastic process V = (Vt)t≥0 is called a gen-eralised Ornstein–Uhlenbeck process if it is of theform Vt = e−ξt

(V0 +

∫ t0 eξs− dηs

)for some bivariate

Levy process (ξ, η), which is independent of V0. Ifthe marginal stationary distribution of this processexists, then its law can be expressed in the formL(

∫ t0 e−ξs− dLs). Here, (ξ, L) is another bivariate Levy

process, constructed from (ξ, L). In this talk we shallstudy the distribution

µc,k,q,r := L(∫ t

0c−Ns− dLs

)in detail in the case when (N, L) is a bivariate com-pound Poisson process without drift and Levy measurebeing concentrated on the three points (1, 0), (0, 1) and(1, c−k), where c > 1 and k in an integer. The param-eters q and r denote the mass of the normalized Levymeasure of (N, L) at the points (1, 0) and (1, c−k), re-spectively. A complete characterization of infinite di-visibility of µc,k,q,r is obtained in terms of the parame-ters c, k, q, r, which depends in particular on algebraicproperties of c. We also study continuity properties ofµc,k,q,r, and show that even in the case when r = 0, i.e.when N and L are independent, absolute continuity de-pends in an intrinsic way on the constant c and on theratio of the rates of the Poisson processes L and N.

The talk is based on [1] and [2].

55

[1] A. Lindner and K. Sato, Continuity propertiesand infinite divisibility of stationary distributionsof some generalized Ornstein–Uhlenbeckprocesses. Ann. Probab., 37, 250–274 (2009).

[2] A. Lindner and K. Sato, Properties of stationarydistributions of a sequence of generalizedOrnstein–Uhlenbeck processes. Math. Nachr., toappear.

Properties of Fractional SchrodingerOperators by Functional IntegrationMethodsJozsef LORINCZI (Loughborough University,UK)

Fractional Schrodinger operators are obtained asoperator or form sums of the fractional Laplacian anda multiplication operator called potential. I will use(fractional) Kato-decomposable potentials to derive afunctional integral representation for semigroups gen-erated by fractional Schrodinger operators involvingsymmetric stable processes. Then I will discuss in-trinsic ultracontractivity and ground state properties ofsuch operators and semigroups. Finally, I will addressexistence, uniqueness and support properties of Gibbsmeasures on stable processes, and discuss some appli-cations in relativistic quantum field theory.

Clique number of high-dimensional ran-dom geometric graphsGabor LUGOSI (Pompeu Fabra University)

We study the behavior of random geometric graphsin high dimensions. We show that as the dimensiongrows, the graph becomes similar to and Erdos-Renyirandom graph. We pay particular attention to theclique number of such graphs and show that it is veryclose to that of the corresponding Erdos-Renyi graphwhen the dimension is larger than log3 n where n isthe number of vertices. The problem is motivated by astatistical problem of testing dependencies.

More about limits of nested subclassesof classes of infinitely divisible distribu-tionsMakoto MAEJIMA (Keio University)

Let I(Rd) be the class of infinitely divisible distribu-tions on Rd and X(µ)

t , t ≥ 0 a Levy process on Rd withL

(X(µ)

1

)= µ ∈ I(Rd), where L(X) denotes the law of a

random variable X.We define a mapping from a subclass D of I(Rd),

which is the domain of the mapping, into I(Rd) by

Φ f (µ) = L(∫ ∞

0f (t)dX(µ)

t

), µ ∈ D.

Many known subclasses of I(Rd) have been character-ized as the ranges of mappings with suitably chosenf ’s.

There are many interesting problems related to thesemappings. In this talk, I pick up one problem that isto find the limits of ranges of these mappings by theiriterations. Even if the original subclasses are different,many different mappings give us one limit of nestedsubclasses given by the iterations of the mappings. Itis the closure of the class of stable distributions on Rd,as shown in [1].

Then a next natural problem is whether the closureof the class of stable distributions is only one class ap-pearing as the limit given by such a procedure. Wecan construct several mappings which produce differ-ent classes as their limits.

References

[1] M. Maejima and K. Sato, The limits of nested sub-classes of several classes of infinitely divisible distri-butions are identical with the closure of the class ofstable distributions. Probab. Theory Relat. Fields 145(2009), 119–142.[2] M. Maejima and Y. Ueda, Compositions of map-pings of infinitely divisible distributions with applica-tions to finding the limits of some nested subclasses,Elect. Comm. in Probab. 15 (2010), 227–239.[3] M. Maejima and Y. Ueda, Nested subclasses ofthe class of α-selfdecomposable distributions, preprint(http://arxiv.org/abs/1006.1047), 2010.

Strong ergodicity and spectral propertyfor Markov processesYong-Hua MAO (School of Mathematical Sci-ences, Beijing Normal University)

In this talk, we present estimates of convergencerate in strong ergodicity for Markov processes, by us-ing a newly founded renewal formula. These estimates

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are connected to the convergence rates in exponen-tial ergodicity, so that we can derive some interest-ing spectral property for Markov semigroups and theirgenerators. These results are applied to some classicalMarkov processes, such as birth and death process anddiffusion processes on Riemannian manifolds.

Threshold networks with randomweights and their extension to spatialnetworksNaoki MASUDA (University of Tokyo)

In the so-called threshold network (graph), each ver-tex is assumed to be equipped with a random weight ofreal value and two vertices are connected if the sum ofthe two weights exceeds a predefined threshold value.The weight is independent for different vertices. Thisnetwork becomes a scale-free network (i.e., power-lawdegree distribution) for various weight distributions,not only for those obeying the power law. I show thisresult and other structural properties of the network bymean-field (physics-type) arguments. Then, I presentmathematical limit theorems that are proved using thevon Mises’ statistics. Next, I extend the model suchthat vertices are embedded in the Euclidean space. Thetwo vertices are now connected iff a function of thetwo weights and the Euclidean distance between thetwo vertices exceeds a predefined threshold. Usually,a pair of vertices is assumed less likely to be connectedif they are more distant from each other. Such a situ-ation seems to be realistic for many real networks in-cluding Internet, and a subclass of this model has beenknown as the gravity model used in various branchesof social science. For this spatial random network, weshow the degree distribution and other structural prop-erties by mean-field arguments. Rigorously provingsome important properties of this model remains anopen problem.

On the value-distribution of log L andL’/LKohji MATSUMOTO (Graduate School of Math-ematics, Nagoya University)

Let L(s, χ) be an L-function associated with a cer-tain character χ. The basic field may be a func-tion field, or a number field. Our main results canbe summarized that a certain average of the value of

log L(s, χ), or L′/L(s, χ), can be expressed as an inte-gral involving a suitable density function. When theaverage is with respect to t = =s, this type of resultgoes back to the classical work of Bohr and Jessen,but we also discuss the case when the average is run-ning over a certain class of characters. Needless to say,the most difficult situation happens when one consid-ers the behaviour of the L-function in the critical strip,and in this case, several mean value theorems are nece-sary to overcome the difficulty. (This is partially a jointwork with Professor Yasutaka Ihara.)

Real Wishart matrices and Haar-distributed orthogonal matricesSho MATSUMOTO (Graduate School of Mathe-matics, Nagoya University)

Let d be a positive integer and let Ω = Sym+(d) bethe open convex cone of d × d positive definite realsymmetric matrices. Let β be a positive real numberin 12 ,

22 , . . . ,

d−12 t ( d−1

2 ,+∞), and let σ = (σi j)1≤i, j≤d

be a matrix in Ω. A real Wishart matrix W in Ω withparameters (β, σ) is defined by its moment-generatingfunction

E[etr(θW)] = det(I − θσ)−β,

where θ is any d × d symmetric matrix such thatσ−1 − θ ∈ Ω. We write W ∼ Wd(β, σ;R).

Let W = (Wi j)1≤i, j≤d ∼ Wd(β;σ;R) and let W−1 =

(W i j)1≤i, j≤d be its inverse. Our main purpose in thistalk is to compute general moments

E[Wk1k2 Wk3k4 · · ·Wk2n−1k2n ], (8)

E[Wk1k2 Wk3k4 · · ·Wk2n−1k2n ], (9)

for any indices k1, k2, . . . , k2n ∈ 1, 2, . . . , d.To describe our main result, we need perfect match-

ings. A perfect matching m on the set 1, 2, . . . , 2nis an unordered pairing of letters 1, 2, . . . , 2n. Denoteby M(2n) the set of all such perfect matchings. Forexample,M(4) consists of three elements

1, 2, 3, 4, 1, 3, 2, 4, 1, 4, 2, 3.

The first moment (8) is given by the sum

2−n∑

m∈M(2n)

(2β)κ(m)∏p,q∈m

σkpkq .

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Here κ(m) is a simple function onM(2n) and runs over1, 2, . . . , n. For example, we have

E[Wk1k2 Wk3k4 ] =β2σk1k2σk3k4 +β2σk1k3σk2k4

+β2σk1k4σk2k3 .

The second moment (9) for the inverse real Wishartmatrix W−1 is more difficult. Set γ = β − d+1

2 and sup-pose γ > n − 1. We have the following formula: theaverage on (9) is equal to

(−1)n2n∑

m∈M(2n)

Wg(m;−2γ)∏p,q∈m

σkpkq .

Here M(2n) 3 m 7→ Wg(m; z) ∈ R, with a real pa-rameter z, is a representation-theoretic function, calledthe orthogonal Weingarten function. For example, wehave

E[Wk1k2 Wk3k4 ] =1

γ(γ − 1)(2γ + 1)((2γ − 1)σk1k2σk3k4

+ σk1k3σk2k4 + σk1k4σk2k3).

On the other hand, we also deal with another ran-dom matrix. Let N be a positive integer and let

O(N) = O ∈ GL(N,R) | OOt = I

be the real orthogonal group of degree N. Itis equipped with the Haar measure dO such thatd(O1OO2) = dO for fixed O1,O2 ∈ O(N) and that∫

O(N) dO = 1.Let O = (Oi j)1≤i, j≤N be a Haar-distributed ma-

trix from O(N). The development in [Collins-Sniady2006] and [3] gives a formula

E[Oi1 j1 Oi2 j2 · · ·Oi2n j2n ]

=∑

m,n∈M(2n)

Wg(m−1n; N)

∏p,q∈m

δip,iq

∏p,q∈n

δ jp, jq

for any i1, . . . , i2n, j1, . . . , j2n ∈ 1, 2, . . . ,N. For ex-ample, we have

E[O1,k1 O1,k2 O2,k3 O2,k4 ] =1

N(N + 2)(N − 1)× (

(N + 1)δk1k2δk3k4 − δk1k3δk2k4 + δk1k4δk2k3

).

Thus, amazingly, the function Wg(·; ·) appears intheories of a inverse real Wishart matrix and a Haar-distributed orthogonal matrix. We talk about this re-semblance.

[1] S. Matsumoto, General moments of theinverse real Wishart distribution and orthogonalWeingarten functions, arXiv:1004.4717v2.

[2] S. Matsumoto, Jucys-Murphy elements,orthogonal matrix integrals, and Jack measures,arXiv:1001.2345v1.

[3] B. Collins and S. Matsumoto, On some propertiesof orthogonal Weingarten functions, J. Math.Phys. 50 (2009), 113516.

Fluctuations of the Ginzburg-LandauModel and Universality for SLE(4)Jason P. MILLER (Stanford University)

The object of our study is the massless field withstrictly convex nearest neighbor interaction on latticeapproximations of a bounded, smooth, planar domainD. This is a general model for a (2+1)-dimensional ef-fective interface. We show that linear functionals ofthe height of the interface converge to the Gaussianfree field on D, a conformally invariant random dis-tribution, and that the mean height becomes harmonicin the limit. We also show that the chordal zero con-tours converge to variants of SLE(4), a family of con-formally invariant random curves.

New perspectives on the HJB equationarising in portfolio choice in incompletemarketsSergey NADTOCHIY (University of Oxford)

Characterizing and constructing the value functionin stochastic optimization problems of optimal portfo-lio choice is a long standing problem. In this talk, Iwill discuss a new method based on a splitting schemefor the associated Hamilton-Jacobi-Bellman equationin a two-factor stochastic model for the stock price.The scheme has the desired consistency and con-vergence properties. This solution approach offers,among others, insightful observations on how marketincompleteness is processed and how it affects the ’infinitesimal ’risk preferences.This is joint work with THALEIA ZA-RIPHOPOULOU

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Connection probabilities and RSW-typebounds for the two-dimensional FKIsing modelPierre NOLIN (Courant Institute, New York Uni-versity)

For two-dimensional independent percolation,Russo-Seymour-Welsh (RSW) bounds on crossingprobabilities are an important a-priori indication ofscale invariance, and they turned out to be instru-mental to describe the phase transition. They are inparticular a key tool to derive the so-called scaling re-lations, that link the critical exponents associated withthe main macroscopic functions.

In this talk, we prove RSW-type uniform bounds oncrossing probabilities for the FK Ising model at crit-icality, independent of the boundary conditions. Acentral tool in our proof is Smirnov’s fermionic ob-servable for the FK Ising model, that makes some har-monicity appear on the discrete level, providing pre-cise estimates on boundary connection probabilities.We also prove several related results – including somenew ones – among which the fact that there is no mag-netization at criticality, tightness properties for the in-terfaces, and the value of the half-plane one-arm expo-nent.

This is joint work with H. Duminil-Copin and C.Hongler.

Displacement convexity of generalizedrelative entropiesShin-ichi OHTA (Department of Mathematics, Ky-oto University)

We introduce the m-relative entropy associated withthe Tsallis entropy as well as the Bregman divergence.As the limit, 1-relative entropy recovers the usual rela-tive entropy (or the Kullback-Leibler divergence). Weshow that, on a weighted Riemannian manifold, theconvexity of the m-relative entropy is equivalent tothe combination of the nonnegativity of the weightedRicci curvature and the convexity of a certain weightfunction (like Lott, Sturm and Villani’s curvature-dimension condition). This curvature bound impliesseveral functional inequalities and the contraction ofthe associated porous medium/fast diffusion equation.This is joint work with Asuka Takatsu (Tohoku Uni-versity).

The Role of the Arcsine Distribution inInfinite DivisibilityVictor PEREZ-ABREU (Center for Research inMathematics CIMAT)

The arcsine distribution is not infinitely divisiblewith respect to classical and free convolutions. How-ever, it plays an important role in the constructionof classical and free infinitely divisible distributions.This talk will we present a survey of this role of thearcsine distribution including known and recent re-sults.

An impulse control approach to optimalorder execution with market price im-pactHuyen PHAM (University Paris Diderot)

We study the optimal portfolio liquidation problemover a finite horizon in a limit order book with bid-askspread and temporary market price impact penalizingspeedy execution trades. We use a continuous-timemodeling framework with strictly increasing discretetrading times, and this is formulated as an impulsecontrol problem under a solvency constraint, includ-ing the lag variable tracking the time interval betweentrades. The associated dynamic programming equa-tion (DP) is a quasi-variational inequality (QVI) satis-fied by the value function in the sense of constrainedviscosity solutions. By taking advantage of the lagvariable tracking the time interval between trades, wecan provide an explicit backward numerical schemefor the time discretization of the DPQVI. The conver-gence of this discrete-time scheme is shown by vis-cosity solutions arguments. An optimal quantizationmethod is used for computing the (conditional) ex-pectations arising in this scheme. Numerical resultsare presented by examining the behaviour of optimalliquidation strategies, and comparative performanceanalysis with respect to some benchmark executionstrategies. We also illustrate our optimal liquidationalgorithm on real data, and observe various interestingpatterns of order execution strategies. Finally, we pro-vide some numerical tests of sensitivity with respect tothe bid/ask spread and market impact parameters.

Based on joint works with: I. Kharroubi, F. Guil-baud, and M. Mnif.

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On Generalized Malliavin CalculusBoris L ROZOVSKY (Brown University)

Traditionally, the starting point in the developmentof Malliavin calculus is the isonormal Gaussian pro-cess (also known as Gaussian white noise) W. For ex-ample, the Malliavin divergence operator defines Sko-rkhod integral with respect to the white noise W. Inthis talk, we discuss a Malliavin type divergence op-erator with respect to linear combinations of elementsof the Cameron-Martin basis generated by W. Theseseries might diverge in L2 (Ω) and therefore shouldbe viewed as generalized random fields. Malliavinderivatives and Ornstein-Uhlenbeck operators will bediscussed as well. This extension of Malliavin calcu-lus is motivated by the recent developments in the the-ory of stochastic PDE, in particular bi-linear ellipticand parabolic SPDEs driven by isotropic white noise.The talk is based on the joint work with S. Lototskyand D. Selesi.

Some aspects of directed edge rein-forced random walksChristophe SABOT (Universite Lyon 1)

Random walks in Dirichlet environments corre-spond to an iid random environment where at eachsite the environment is chosen according to a Dirich-let law. The annealed law corresponds to the law of areinforced random walks where the counter is on di-rected edges. This model shows some interesting an-alytical simplifications which are all due to a propertyof statistical invariance by time reversal. In this talk Iwill explain this property and some of its applicationsto transience and to the environment viewed from theparticule.

Lace expansion in the past and futureAkira SAKAI (Creative Research InstitutionSOUSEI, Hokkaido University)

The lace expansion is one of the few tools to inves-tigate critical behavior mathematically rigorously. Itwas initiated by Brydges and Spencer in 1985 to provemean-field critical behavior for weakly self-avoidingwalk above 4 dimensions. Since then, the method-ology has been developed and successfully appliedto various statistical-mechanical models, such as ori-

ented/unoriented percolation, lattice trees/lattice ani-mals, the contact process and the Ising model.

In this talk, I will survey the recent development ofthe lace expansion since I became involved in 2000,and discuss potential future problems.

Transition probability densities of LevyprocessesRene L SCHILLING (TU Dresden, Department ofStochastics)

We discuss several necessary and sufficient condi-tions for the existence of (smooth) transition proba-bility densities for Levy processes and isotropic Levyprocesses. Under some mild conditions on the char-acteristic exponent we calculate the asymptotic be-haviour of the transition density as t tends to zero reso.infinity and show a ratio-limit theorem.

On nearly optimal strategies for risk-sensitive portfolio optimization on infi-nite horizonJun SEKINE (Graduate School of Engineering Sci-ence, Osaka University)

Risk-sensitive portfolio optimization on infinitehorizon is discussed with a linear Gaussian factormodel. Results in Fleming and Sheu (1999) andKuroda and Nagai (2002) are strengthened: Whenagent is too risk-averse, the verification of the can-didate strategy can fail, although the stabilizing so-lution to the associated ergodic HJB equation alwaysexists. (Even worse, the associated risk-sensitized ex-pected growth rate for the candidate strategy can be−∞.) Nevertheless, the optimal value is always finiteand nearly optimal strategies are constructed.

Optimal investment on finite horizonwith random discrete order flow in illiq-uid marketsMihai SIRBU (University of Texas)

We study the problem of optimal portfolio selectionin an illiquid market with discrete order flow. In thismarket, bids and offers are not available at any time buttrading occurs more frequently near a terminal hori-zon. The investor can observe and trade the risky assetonly at exogenous random times corresponding to the

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order flow given by an inhomogenous Poisson process.By using a direct dynamic programming approach, wefirst derive and solve the fixed point dynamic program-ming equation and then perform a verification argu-ment which provides the existence and characteriza-tion of optimal trading strategies. We prove the con-vergence of the optimal performance, when the deter-ministic intensity of the order flow approaches infinityat any time, to the optimal expected utility for an in-vestor trading continuously in a perfectly liquid mar-ket model with no-short sale constraints. Joint workwith Paul Gassiat and Huyen Pham.

Random Point Processes and WignerMatricesAlexander B. SOSHNIKOV (University of Cal-ifornia at Davis)

My talk will consist of two parts.In the first part, I will talk about the recent results

of my Ph.D. student, Sean O’Rourke, on the Gaus-sian fluctuation of eigenvalues in Wigner random ma-trices. O’Rourke extended the CLT obtained by J.Gustavsson for the Gaussian Unitary Ensemble firstto the Gaussian Orthogonal and Gaussian Symplec-tic Ensembles and then to a sufficiently wide classof Wigner real symmetric random matrices. Gustavs-son’s approach relied on the Costin-Lebowitz theoremfor determinantal random point processes. To extendthe results to the GOE/GSE O’Rourke used the rela-tions between unitary, orthogonal, and symplectic en-sembles due to Forrester and Rains. Finally, he useda variant of the Tao-Vu Four Moment Theorem to ex-tend the results to Wigner real symmetric matrices.

In the second part of my talk, I will discuss a re-solvent approach to the universality problem in ran-dom matrices. In particular, I will discuss recent jointresults with my Ph.D. students David Renfrew andPierre Dueck on the largest eigenvalues for finite rankperturbations of Wigner matrices.

Some Diffusion Processes AssociatedWith Two Parameter Poisson-DirichletDistribution and Dirichlet ProcessWei SUN (Concordia University)

The two parameter Poisson-Dirichlet distributionPD(α, θ) is the distribution of an infinite dimensional

random discrete probability. It is a generalization ofKingman’s Poisson-Dirichlet distribution. The twoparameter Dirichlet process Πα,θ,ν0 is the law of a pureatomic random measure with masses following thetwo parameter Poisson-Dirichlet distribution. In thistalk we focus on the construction and the propertiesof the infinite dimensional symmetric diffusion pro-cesses with respective symmetric measures PD(α, θ)and Πα,θ,ν0 . The methods used come from the theoryof Dirichlet forms. This talk is based on joint workwith Shui Feng, Feng-Yu Wang and Fang Xu.

Piecewise Deterministic Processes andintrinsic fluctuations of neuronal activ-ityMichele Marie THIEULLEN (Laboratoire deProbabilites et Modeles Aleatoires Universite Pierre etMarie Curie-Paris 6)

In this talk we first recall main properties of Piece-wise Deterministic Processes and we present limit the-orems for sequences of such processes. We then applythese results to study the impact of the stochastic be-haviour of ion channels on the membrane potential ofa neuron when the number of channels is large but fi-nite.

Scaling limits of self-interacting randomwalks and diffusionsBalint TOTH (Budapest University of Technology,Institute of Mathematics)

I will present a survey of recent results aboutthe long time asymptotic behaviour of random pro-cesses with long memory due to some rather natu-ral local self-intaraction (self-repellence) of the tra-jectories. Typical examples are the so-called myopic(or ”true”) self-avoiding random walk and the self-repelling Brownian polymer models. The long timeasymptotics of the displacement is expected to be ro-bust (not depending on some microscopic details), butdimension dependent. It is expected that in 1d the mo-tion is strongly superdiffusive, with time-to-the-two-thirds scaling; in 2d the motion is marginally superdif-fusive with logarithmic multiplicative correction in thescaling; in three and more dimensions the displace-ment is diffusive. For some particular models someof these conjectures have been proved. The talk will

61

be based on joint work with P. Tarres and B. Valko,respectively, with I. Horvath and B. Veto.

Second Order backward SDEsNizar TOUZI (Ecole Polytechnique Paris)

We provide an existence and uniqueness theory foran extension of backward SDEs to the second order.While standard Backward SDEs are naturally con-nected to semilinear PDEs, our second order exten-sion is connected to fully nonlinear PDEs. In par-ticular, we provide a fully nonlinear extension of theFeynman-Kac formula. Unlike the previous definitionin Cheridito, SOner, Touzi and Victoir, the alterna-tive formulation of this paper insists that the equationmust hold under a non-dominated family of mutuallysingular probability measures. The key argument isa stochastic representation, suggested by the optimalcontrol interpretation.

Statistical estimation of the volatility fora stochastic differential equationMasayuki UCHIDA (Graduate School of Engi-neering Science, Osaka University)

We consider the statistical estimation problem of thevolatility parameter for a multidimensional Ito processbased on high frequency data observed on a fixed timeinterval. Asymptotic theory of the maximum like-lihood type estimator for a volatility parameter of adiffusion process has been developed, see for exam-ple, [1]. In this talk, we study asymptotic mixed nor-mality (stable convergence) and convergence of mo-ments of both the maximum likelihood type estima-tor and the Bayes type estimator for the volatility pa-rameter of the Ito process. In order to obtain theresults, we use the Ibragimov-Has’minskii-Kutoyantsprogram with the polynomial type large deviation in-equality for the statistical random field by [2]. Fur-thermore, the non-degeneracy of the statistical randomfield is indispensable for the large deviation inequality.In spite of its importance, it has not been investigatedso far in the non-ergodic statistics for stochastic differ-ential equations involving random Fisher information.We present useful criteria for it.

This is a joint work with Nakahiro Yoshida.

[1] Genon-Catalot, V. and Jacod, J., On the estimationof the diffusion coefficient for multidimensionaldiffusion processes. Ann. Inst. Henri PoincareProbab. Statist. 29, 119–151, (1993).

[2] Yoshida, N., Polynomial type large deviationinequalities and quasi-likelihood analysis forstochastic differential equations. To appear inAnn. Inst. Statist. Math.

Scaling limits for critical epidemics andrandom graphsJohan VAN LEEUWAARDEN (TU Eindhovenand EURANDOM)

We investigate, in the critical regime, the finalsize distribution in SIR epidemic models, as well asthe largest connected component in inhomogeneousErdos-Renyi random graphs. We derive new scalinglimits, and analyze both new and existing scaling lim-its, including Brownian motion with parabolic driftand a ‘thinned’ Levy process.

Multidimensional branching randomwalk with branching at the origin onlyVladimir Alekseevich VATUTIN (SteklovMathematical Institute)

A continuous time branching random walk on the d-dimensional lattice is considered in which individualsmay produce children at the origin only.

Assuming that the underlying random walk is sym-metric and the offspring reproduction law is criticalwe study the asymptotic behavior of the probability ofsurvival of this process, the expected number of indi-viduals at the origin, the probability that there are in-dividuals at the origin at moment t → ∞ and the jointdistribution of the number of individuals at the originand outside the origin at moment t → ∞.

It is shown that the respective statements are essen-tially different for the cases of dimensions 1 ≤ d ≤ 2,3 ≤ d ≤ 5, d = 6 and d ≥ 7.

Spatial Lambda-Fleming-Viot processand associated genealogiesAmandine VEBER (University Paris-Sud 11)

A spatial Lambda-Fleming-Viot process models apopulation distributed on Rd (R2 in practice) which ex-

62

periences local partial extinctions, followed by the re-colonization of the affected area by the offspring of anindividual present in this region. After introducing themodel and some of its properties, we will consider thegenealogy of a sample of individuals when the popu-lation lives on a two-dimensional torus of side L. Inparticular, we will see that this ancestral process con-verges as L grows to infinity towards a coalescent withmultiple mergers, whose characteristics depend on therange of the extinction areas (joint work with AlisonEtheridge).

Single–crossover recombination andancestral recombination treesUte VON WANGENHEIM (Bielefeld Univer-sity)

Modeling the process of recombination leads to alarge coupled nonlinear dynamical system that is no-toriously difficult to treat. In my talk, I will present amodel that describes recombination in an infinite pop-ulation with single crossovers only. I will highlightsome special properties of the dynamics and the par-ticular difficulties that come along with the dependen-cies implied by discrete time.

The quantities that define the solution admit astochastic interpretation and I will state these by de-scribing the process of recombination backwards intime, i.e. by backtracking the evolution of the variousindependent segments each type is composed of. Thisresults in binary tree structures, which can be used as atool to formulate an explicit solution of the dynamics.[1] von Wangenheim, U., Baake, E., Baake, M.

Single–crossover recombination in discrete timeJ. Math. Biol 60, 727–760 (2010).

A Stochastic Model of Coupled Enzy-matic ProcessingRuth WILLIAMS (University of California, SanDiego)

A major challenge for systems biology is to de-duce the molecular interactions that underly correla-tions observed between concentrations of different in-tracellular molecules. While direct explanations suchas coupled transcription/translation or direct protein-protein interactions are often considered, potential in-direct sources of coupling have received much less at-tention. In this talk, I will report on an investigation,

involving both a stochastic model and related experi-ments, of how correlations can arise generically fromsuch an indirect coupling mechanism involving theprocessing of multiple protein species by a commonenzyme.

Based on joint work with Natalie Cookson, JeffHasty, Will Mather, Octavio Mondragon-Palomino,Lev Tsimring.

Extremality of excursion measure and ofσ-finite measure unifying penalisationsKouji YANO (Kobe University)

The excursion measure for Brownian motion maybe decomposed into the sum of those for positive andnegative reflected Brownian motions, which are ex-tremal points in the class of entrance laws for Brown-ian motion killed at zero. Remark that extremality isequivalent to irreducibility and to germ-triviality.

In this talk, we discuss the following two topics.(1) Extremality of the excursion measure for sym-

metric Levy process. It is proved in [3] that the excur-sion measure for stable Levy process of index 1 < α <2 is extremal, while it is not the case if α = 2.

(2) Extremality of σ-finite measure unifying penal-isations. Najnudel, Roynette and Yor ([1] and [2])introduced a remarkable σ-finite measure which uni-fies the long-time limit of Wiener measure weightedby some adapted functionals and normalized. KoujiYano–Yuko Yano–Yor ([4]) obtained analogous resultsfor symmetric stable Levy processes. We discuss ex-tremality of this measure in the class of exit family.

[1] J. Najnudel, B. Roynette and M. Yor. A globalview of Brownian penalisations, MSJ Memoirs,19, Mathematical Society of Japan, Tokyo, 2009.

[2] B. Roynette and M. Yor. Penalising Brownianpaths, Lecture Notes in Mathematics, 1969,Springer-Verlag, Berlin, 2009,

[3] K. Yano. Excursions away from a regular pointfor one-dimensional symmetric Levy processeswithout Gaussian part. Potential Anal., 32, no. 4,305–341, 2010.

[4] K. Yano, Y. Yano and M. Yor. Penalisingsymmetric stable Levy paths, J. Math. Soc.Japan, 61, no. 3, 757–798, 2009.

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On transformation of Markov processesJiangang YING (Department of Mathematics, Fu-dan University)

This talk will give a survey for the progress ontransformation-killing transform, time change, drfttransform, of symmetric Markov processes, after thepublication of Fukushima-Oshima-Takeda’s book in1995.

Quantum Physics and Stochastic Defor-mationJean Claude ZAMBRINI (GFM,University Lis-bon)

It is well known that Quantum Physics is not a reg-ular probabilistic theory.All attempts to prove the con-trary have failed.However,Feynman’s heuristic inter-pretation of Quantum physics as a stochastic deforma-tion of Classical Physics can (and should) indeed bepreserved.The key step is to time symmetrize Stochas-tic Analysis,in a way more general than the one knownby probabilists.Then new structures appear, showingmuch closer relations between the two frameworks.We shall describe some recent results of the programknown as ”Stochastic Deformation” showing in whatextent basic tools of Stochastic Analysis can be rein-terpreted in quantum terms and,reciprocally,basic as-pects of Quantum Physics can be better understoodthrough methods of Stochastic Analysis.The point ofthe whole program is to provide,on both sides,newproblems (and answers) in directions ignored by thosetwo fields considered independently.

Monte Carlo Methods for High Dimen-sional BSDEs and PDEsJianfeng ZHANG (University of Southern Cali-fornia)

Due to its importance in applications, numericalmethods for Backward SDEs and their associatedPDEs have received very strong attention in the pastdecade. There are typically two approaches, the PDEapproach and the Monte Carlo approach. While effi-cient in low dimensions, the PDE approach does notwork for high dimensional problems, due to the wellknown curse of dimensionality. In this talk we will in-troduce the Monte Carlo approach for BSDEs, which

works well for reasonably high dimensional problems.We will also discuss briefly the recent developmenton second order backward SDEs, which is associatedwith a fully nonlinear parabolic PDE.

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Organized Contributed SessionsMaximum principle for controlledstochastic partial differential equationAbdulRahman Soliman AL-HUSSEIN (Qas-sim University)

In this talk we shall study an infinite dimensionalcontrolled stochastic partial differential equation. Theequation is driven by a continuous martingale in a sep-arable Hilbert space and a time-dependent unboundedlinear operator A(t), t ≥ 0.

We shall derive a maximum principle for this sys-tem by using the adjoint backward stochastic partialdifferential equation.

Odds theorem with multiple selectionchancesKatsunori ANO (Institute of Applied Mathemat-ics)

We study the multi-selection version of the so-called odds theorem by Bruss ((2000) Ann. Probab.28, pp.1384-1391). We observe a finite number of in-dependent 0/1 (failure/success) random variables se-quentially and want to select the last success. We de-rive the optimal selection rule when m (≥ 1) selectionchances are given and find that the optimal rule hasthe form of a combination of multiple odds-sums. Weprovide a formula for computing the maximum proba-bility of selecting the last success when we have m se-lection chances and also provide closed-form formulasfor m = 2 and 3. For m = 2, we further give the boundsfor the maximum probability of selecting the last suc-cess and derive its limit as the number of observationsgoes to infinity. An interesting implication of our re-sult is that the limit of the maximum probability of se-lecting the last success for m = 2 is consistent with thecorresponding limit for the classical secretary problemwith two selection chances. This is a joint work withHideo Kakinuma and Naoto Miyoshi, Tokyo Instituteof Technology.

Shooting Methods For Numerical Solu-tion of Linear and Nonlinear StochasticBoundary-Value ProblemsArmando ARCINIEGA (Department of Mathe-matics The University of Texas at San Antonio)

Numerical methods are developed for approximatesolution of linear and nonlinear stochastic boundary-value problems. First, a shooting method procedureis examined for numerically solving a linear systemof Stratonovich boundary-value problems. Then, theshooting method procedure is described for numer-ically solving non linear stochastic boundary-valueproblems. These stochastic shooting methods are anal-ogous to standard shooting methods fornumerical so-lution of ordinary deterministic boundary-value prob-lems. It is shown that the shooting methods provideaccurate approximations. Error analysis areperformedand computationalsimulations are described.

LND of multiparameter mfBmAntoine AYACHE (Laboratory Paul Painleve,University Lille 1)

This is a joint work with Narn-Rueih Shieh (Na-tional Taiwan University) and Yimin Xiao (MichiganState University).

By using a wavelet method we prove that theharmonisable-type N-parameter multifractional Brow-nian motion (mfBm) is a locally nondeterministic(LND) Gaussian random field. This nice property thenallows us to establish joint continuity of the local timesof an (N, d)-mfBm and to obtain some new results con-cerning its sample path behavior.

Stationary Solutions of GeneralisedOrnstein-Uhlenbeck ProcessesAnita Diana BEHME (TU Braunschweig)

The generalised Ornstein-Uhlenbeck process withstarting random variable V0 driven by some bivariateLevy process (ξt, ηt)t≥0 is defined as

Vt = e−ξt

(V0 +

∫ t

0eξs−dηs

), t ≥ 0.

It is the unique solution of the stochastic differentialequation

dVt = Vt−dUt + dLt, t ≥ 0

where (Ut, Lt)t≥0 is a bivariate Levy process com-pletely determined by (ξt, ηt)t≥0.If V0 is chosen to be independent of (ξt, ηt)t≥0, the

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process (Vt)t≥0 is called causal. Stationary solutionsof causal generalised Ornstein-Uhlenbeck processeshave been studied by Lindner and Maller [LM] in de-tail.In this talk we dispose of the causality condition andgeneralise the results of Lindner and Maller by prov-ing the existence of non-causal stationary solutions ofVt.We present these stationary solutions and then discussthe necessary changement of the underlying filtrationwhich is needed to give sense to the occuring stochas-tic integrals.Finally some second-order properties as expectationand autocovariance function of the stationary solutionsand results on their tail-behaviour will be shown.

This talk is based on [BLM] and [B].[B] Behme, A.: Distributional properties of stationary

solutions of dVt = Vt−dUt + dLt with Levy noise.Preprint

[BLM] Behme, A., Lindner, A. and Maller, R.:Stationary solutions of the stochastic differentialequation dVt = Vt−dUt + dLt with Levy noise.Stochastic Process. Appl., submitted

[LM] Lindner, A.; Maller, R.: Levy integrals andthe stationarity of generalised Ornstein-Uhlenbeckprocesses. Stochastic Process. Appl., 115, no. 10,1701-1722, (2005).

Schroedinger perturbations of transi-tion densitiesKrzysztof BOGDAN (Wroclaw University ofTechnology)

We construct transition densities under perturba-tions with a certain integral space-time relative small-ness. My talk will report on a joint work with W.Hansen and T. Jakubowski.

General structures of a class of stochas-tic models with two-sided jumpsEric CHEUNG (Department of Statistics and Ac-tuarial Science, University of Hong Kong)

In this talk, we consider a stochastic process in-volving two-sided jumps and a continuous downwarddrift. In the context of ruin theory, it represents the

surplus process of a business enterprise which is sub-ject to constant expense rate over time along with ran-dom gains and losses. The key quantity of our interestis (a variant of) the Gerber-Shiu expected discountedpenalty function (Gerber and Shiu (1998)) widely usedin insurance risk theory. Leaving the distributions ofthe jump sizes and their inter-arrival times arbitrary,the general structure of the Gerber-Shiu function isstudied via an underlying ladder height structure anda Markov renewal equation. Applications include, forexample, the joint Laplace transform of time of ruin,time of recovery and first duration of negative surplus.Since the stochastic process is also related to a queue-ing system with instantaneous work removal (or neg-ative customers), quantities such as the joint Laplacetransform of the busy period and the subsequent idleperiod can be obtained from the Gerber-Shiu functionas well. If time permits, further analysis is conductedonly assuming the upward jumps follow a combinationof exponentials.

Affine processes on symmetric conesChrista CUCHIERO (ETH Zuerich)

We consider stochastically continuous affine pro-cesses on pointed convex cones and derive necessaryadmissibility conditions on the involved parameters.We study in particular the case of irreducible symmet-ric cones and give a full characterization of affine pro-cesses thereon.

On controlled branching processes invarying environmentInes Maria DEL PUERTO (Department ofMathematics, Faculty of Sciences, University of Ex-tremadura)

The study of the long-term changes in the numberof individuals in a population is a topic of interest inthe field of population dynamics. Branching processesare regarded as appropriate probability models for thedescription of the extinction/growth of populations. Inparticular, controlled branching processes are useful tomodel some situations where some kind of control isrequired. In the literature on controlled branching pro-cesses the control phase is assumed to depend on thepopulation size. On the other hand, in the vast major-ity of papers, the reproduction law is assumed to be

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the same for every individual in any generation. How-ever, it seems reasonable to think that the reproductiveabilities of a population may vary from one genera-tion to another and also that the control could changewith the generation independently of the populationsize. In this talk we present the controlled branchingprocess in varying environment. For this process, suf-ficient conditions for almost sure extinction and for apositive probability of indefinite growth are provided.Moreover the limit behaviour of the process suitablynormed is studied.

This is a joint work with M. Gonzalez, M. Mota andA. Ramos.

Acknowledgements: This research was supportedby the Ministerio de Ciencia e Innovacion and theFEDER through the Plan Nacional de InvestigacionCientıfica, Desarrollo e Innovacion Tecnologica, grantMTM2009-13248.

The lent particle method and its applica-tionsLaurent DENIS (University of Evry France)

We present a new approach to absolute continuityand regularity of laws of Poisson functionals. Thetheoretical framework is that of local Dirichlet formsand more precisely the (EID) property: Energy Im-age Density property. The method gives rise to a newexplicit calculus that we first show on some simple ex-amples : it consists in adding a particle and taking itback after computing the gradient. This method per-mits to to develop a Malliavin calculus on the Poissonspace and to obtain in a simple way existence of den-sity and regularity of laws of Poisson functionals suchas Levy areas, solutions of SDE’s driven by Poissonmeasure...

→ These talks are based on several joint works withN. Bouleau.

Equation for kernels of integral invari-ants of generalized Ito equations andtheir connection with some equations ofthe stochastic processes theoryValery DOOBKO (National Aviation Univesity,Information-diagnostic Systems Institut)

On the basis of the introducing of concept about in-

tegrating on random manifold [1,2], that are inducedby the solutions x(t, y) ∈ Rn, x(0, y) = y of generalizedIto equations (GEI) and requirement:∫

Rn ρl(x, t) f (x)dV(x) =∫Rn ρl(y) f (x(t, y))dV(y),

ρl(x, 0) = ρl(x),(1)

the equations for ρl(x, t) ( kernels of integral invariantsof GEI) are obtained (l = 1, (n + 1)) [2].

Using (1) and equation for ρl(x, t), the equations forρl(x, t)ρn+1(x, t)

= ui(x, t) (stochastic first integrals of GEI)

are constructed [2].Let z(t, x) ∈ Rm is solution of this GEI equation ,

with a coefficient depending from t, x. Using (1) theequation for ρl(x, t), the stochastic differential of thefunction z(t, x(t, y)) we construct (the generalizationof the formula Ito-Ventsel’s). The return problems ofconstruction of the class GEI, ensuring, for example,condition of conservation of a phase volume, existenceof the determined set of the first integrals are resolved.The examples of the solutions are resulted. [1,3][1] V.A. Doobko, Questions of theory and application

of stochastic differential equations , Vladivostok,1989. (In Russian)

[2] V.A. Doobko, Open evolving systems (Somemathematical aspects of simulation) - 1-stint.sci.and prac.conf. ”Open evolving systems”,Kyev, 2002. P.14-30. (In Russian).

[3] V.A. Doobko, Integral invariants of equations Itoand their connection with some problems of thetheory of stochastic processes. - The Reports ofNat.Ac. of sci. of Ukraine. 2002. P.24-29. (InRussian)

Y-linked bisexual branching processeswith blind choice of mates: Bayesian in-ference through MCMC methodsMiguel GONZALEZ (Department of Mathemat-ics, Faculty of Sciences, University of Extremadura)

It is well-known that in human and some animalpopulations the sex of the individuals is determinedby a pair of chromosomes X and Y. A female has XXchromosomes, while a male has XY chromosomes.Certain characteristics are due to genes carried on theX chromosome (X-linked). Others due to genes car-ried on the Y chromosome (Y-linked) and still oth-ers to genes carried on both chromosome (XY-linked).

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From a practical viewpoint, it is of interest to modeland analyze the evolution of sex-linked genes fromgeneration to generation.

Focusing our attention in the Y-chromosome, it isworth mentioning that most of the Y-linked genes arenot expressed in males or if they are, they do not playany role in the mating of these males. Recently, in [1]it was introduced a two-dimensional bisexual branch-ing process to analyze the evolution of the number ofcarriers of this type of Y-linked genes.

The behaviour of these kinds of genes is stronglyrelated to the reproduction law of each genotype. Inpractice, these offspring distributions are usually un-known and their estimation is necessary. In this paper,we deal with the problem of estimating the offspringdistribution of each genotype of a Y-linked gene whenthe only data we suppose available are the total num-ber of males of each genotype and the total number offemales up to some generation. We set out the problemfrom a Bayesian outlook. We provide an algorithm,based on the Gibbs sampler and gaussian kernel den-sity estimators, to approximate the posterior distribu-tion of the reproduction law of each genotype. Fromthe estimated posterior density, we also obtain HPD(high posterior density) credible regions for the repro-duction mean of each genotype and we approximatethe posterior predictive distribution of the future pop-ulation size. Finally, by way of several simulated ex-amples we illustrate the accuracy of the algorithm in-troduced. These examples have been developed withthe statistical software R.

This is a joint work with C. Gutierrez and R.Martınez.

Acknowledgement: The research was supportedby the Ministerio de Ciencia e Innovacion andFEDER, grant MTM2009-13248.

References:[1] Gonzalez, M., Martınez, R. and Mota, M.

(2009), Bisexual branching processes to modelextinction conditions for Y-linked genes, Journalof Theoretical Biology, 258, 478-488.

Spectral methods for quantum randomwalksF. Alberto GRUNBAUM (Math Dept Universityof California, Berkeley)

The classical work , mainly by Karlin and McGre-gor, dealing with Classical random walks has been re-cently extended to study Quantum random walks injoint work with Cantero, Moral and Velazquez.

I will discuss some new results that are obtained byusing this approach.

Linear Multifractional Stable Motion:Wavelet Methods and Sample pathspropertiesJulien HAMONIER (Universite Lille1)

The Linear Multifractional Stable Motion (LMSM),denoted by Y = Y(t) : t ∈ R, is a Strictly α-Stable(StαS) stochastic process which was introduced in2004 by Taqqu and Stoev [2] with a view to modelsome features of traffic traces on telecommunicationnetworks, typically changes in operating regimes andburstiness (the presence of rare but extremely busy pe-riods of activity). This process is obtained by replac-ing the constant Hurst parameter of the Linear Frac-tional Stable Motion by a function H(·). Throughoutour talk, we will assume that the function H(·) takesvalues in (1/α, 1).

Our goal is to improve some Taqqu and Stoev’s re-sults [3] concerning the sample path behavior of Y; tothis end we will use a wavelet approach which is toa certain extent inspired from that in [1]. More pre-cisely:

(i) It has been shown in [3] that a sufficient condi-tion for the trajectories of Y to be continuous,with probability 1, on a compact interval K , isthat H(·) be a Holder function on K . Also, it hasbeen conjectured in the same article that this suf-ficient condition is not necessary, more precisely:the continuity of the trajectories of LMSM holdsas long as H(·) is continuous. We will prove thatthis Taqqu and Stoev’s conjecture is true.

(ii) Under the same condition, some bounds ofβY (K), the critical uniform Holder exponent ofthe trajectories of Y over K , have been obtainedin [3]; when H(·) belongs to the Holder spaceCβ(K ,R) with β > H∗ := maxH(t), t ∈ K thenthese bounds can be expressed as H∗ − 1/α ≤βY (K) ≤ H∗, where H∗ := minH(t), t ∈ K. Wewill give a sharp modulus of continuity of the tra-jectories of Y and consequently prove that almostsurely (a.s.) βY (K) = H∗ − 1/α.

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[1] Ayache, A., Roueff, F., Xiao, Y., Linearfractional stable sheets: wavelet expansionand sample path properties, Stochastic Process.Appl, 119, 1168-1197, 2009.

[2] Stoev, S., Taqqu, M.S., Stochastic Properties ofthe Linear Multifractional Stable Motion, Adv.Appl. Prob., 34, 1085-1115, 2004.

[3] Stoev, S., Taqqu, M.S., Path Properties of theLinear Multifractional Stable Motion, Fractals,13, 2, 157-178, 2005.

Branching structure for an (L-1) randomwalk in random environment and its ap-plicationsWenming HONG (Beijing Normal University)

By decomposing the random walk path, we con-struct a multitype branching process with immigra-tion in random environment for corresponding ran-dom walk with bounded jumps in random environ-ment. Then we give two applications of the branch-ing structure. Firstly, we specify the explicit invari-ant density by a method different with the one used inBremontand reprove the law of large numbers of therandom walk by a method known as “ the environmentviewed from particles”. Secondly, the branching struc-ture enables us to prove a stable limit law, generalizingthe result of Kesten-Kozlov-Spitzerfor the nearest ran-dom walk in random environment. As a byproduct,we also prove that the total population of a multitypebranching process in random environment with immi-gration before the first regeneration belongs to the do-main of attraction of some κ-stable law.

Uncertain Markov decision processeswith Bayesian intervalsMasayuki HORIGUCHI (Department of Math-mematics, Faculty of Engineering, Kanagawa Univer-sity)

We are concerned with Markov decision processeswith unknown transition matrices, which is called un-certain MDPs. Using Bayesian inference of intervalsof prior measures by De Robertis/Hartigan[1], the truetransition matrix is estimated by an interval matrix.Then, uncertain MDPs of Bayesian approach is de-fined as a controlled Markov set-chain model([2],[3]).We formulate interval estimated MDPs and show the

existence of Pareto-optimal policy. One of interval es-timations of transition matrix is mean value of pos-terior intervals of measures and the other is percentpoint of posterior measures. Some convergence prop-erty and characterization of interval of value functionis discussed. Also, as a numerical example, sequen-tial sampling problem and optimal stopping rule areshown.[1] L. De Robertis and J. A. Hartigan. Bayesian

inference using intervals of measures. Ann.Statist., 9(2):235-244, 1981.

[2] M. Kurano, M. Yasuda, and J. Nakagami. Intervalmethods for uncertain Markov decision processes.In: Markov processes and controlled Markovchains (Changsha, 1999), pages 223-232. Kluwer,2002.

[3] D. J. Hartfiel. Markov set-chains, volume 1695 ofLecture Notes in Mathematics. Springer, 1998.

Sufficient condition for wide-sense sta-tionarity of random harmonic processesElena KARACHANSKAYA (Pacific NationalUniversity Mathematical Modeling and Control Pro-cesses Department)

It is assumed, that a random harmonic processes arewide-sense stationary, if their random phase has a uni-form distribution only.

We determine [1] the conditions for density func-tion of the random phase for the harmonic process bewide-sense stationary.[1] Doobko V. A. SHCS-series and their application

for generalization, classification and simulationof the random harmonic processes : preprint /V. A. Doobko, E. V. Karachanskaya ; Comp.Center FEB RAS. – Khabarovsk : Publ. PNU,2010. (In Russian)

Determinantal Processes and EntireFunctionsMakoto KATORI (Department of Physics, ChuoUniversity)

In the talk by Tanemura, it is proved that the Dysonmodel (Dyson’s Brownian motion model with β = 2)is determinantal in the sense that the moment gener-ating function of any multitime distribution is given

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by a Fredholm determinant associated with a contin-uous kernel. The continuous kernel is given by anintegral transformation of an entire function. In thepresent talk, we discuss the relationship between en-tire functions and particle systems with long-rangedinteractions having finite and infinite numbers of par-ticles. An entire function is characterized by its orderof growth describing global behavior and the distri-bution of zeros describing local behavior of the func-tion. These two aspects of an entire function is re-lated with each other, and the Hadamard theorem givesthe Weierstrass canonical product representation. Inour study the distributions of zeros of the entire func-tions appearing in the correlation kernels of determi-nantal processes are identified with the initial config-urations of the systems. Applying the theory of en-tire functions, time-evolution of the correlation ker-nels and then the non-equilibrium dynamics of infiniteparticle systems with long-ranged interactions can becontrolled by putting appropriate conditions to the ini-tial configurations.

Limit theorems and localization forquantum walks on graphsNorio KONNO (Faculty of Engineering Yoko-hama National University)

Using generating functions, we consider the behav-ior of the discrete-time quantum walk (QW). As forthe QW, see [1]. We present limit theorems of the QWfor a class of graphs. As a corollary, our previous re-sult on trees can be obtained [2]. In addition, we dis-cuss localization for the space-inhomogeneous QW inone dimension.[1] N. Konno, Quantum Walks, Lecture Notes in

Mathematics, 1954, Springer, 309-452 (2008).[2] K. Chisaki, M. Hamada, N. Konno and E. Segawa,

Limit theorems for discrete-time quantum walkson trees, Interdisciplinary Information Sciences,15, 423-429 (2009).

Stochastic equations and Fleming-ViotflowsZenghu LI (Beijing Normal University)

We present some general results on pathwiseuniqueness, comparison property and existence ofnon-negative strong solutions of stochastic equations

driven by white noises and Poisson random measures.The results are used to prove the strong existence ofthe so-called generalized Fleming-Viot flows intro-duced in the study of coalescents with multiple colli-sions. Some scaling limit theorems for the are proved,which lead to sub-critical branching immigration su-perprocesses.

Hitting half-spaces by Bessel-BrowniandiffusionsJacek MALECKI (University of Angers and Wro-claw University of Technology)

Our purpose is to find explicit formulas describ-ing the joint distributions of the first hitting time andplace for half-spaces of codimension one for a dif-fusion in Rn+1, composed of one-dimensional Besselprocess and independent n-dimensional Brownian mo-tion. The most important argument is carried outfor the two-dimensional situation. We show that thisamounts to computation of distributions of various in-tegral functionals with respect to a two-dimensionalprocess with independent Bessel components. As aresult, we provide a formula for the Poisson kernel ofa half-space or of a strip for the operator (I − ∆)α/2,0 < α < 2. In the case of a half-space, this result wasrecently found, by different methods, in Byczkowskiet al. (Trans Am Math Soc 361:4871-4900, 2009). Asan application of our method we also compute variousformulas for first hitting places for the isotropic stableLevy process.

On estimating SDE with jumpsHiroki MASUDA (Graduate School of Mathe-matics, Kyushu University)

We consider a class of discretely but frequentlyobserved stochastic differential equations (SDE) withjumps, the coefficients of which depend on a finite-dimensional parameter. Our purpose here is, based onavailable data, to estimate the unknown parameter. Tothis end, we target the Gaussian quasi-likelihood ran-dom field, and show that it leads to an asymptoticallynormally distributed estimator. Moreover, as an ap-plication of the estimator so obtained, we can test apresence of any nontrivial jump component, based onself-normalized partial sum statistics. Some illustra-tive numerical examples will be given.

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Exponential of stationary processesMuneya MATSUI (University of Tokyo)

We study the correlation decay and the expectedmaximal increment of the exponential process deter-mined by some stationary process, e.g. fractionalOrnstein-Uhlenbeck process, Levy driven CARMAprocess, fractional CARMA process. We also treatour on going project about exponential process givenby the Lamperti transform of a self-similar process,which is stationary. Finally, its perspective role instochastic modelling of finance and telecommunica-tion is discussed. (joint work with Narn-Rueih Shieh)

On strong solutions of positive definitejump-diffusionsEberhard MAYERHOFER (Vienna Institute ofFinance, Vienna University of Economics and Busi-ness)

We show the existence of unique global strong solu-tions of a class of stochastic differential equations onthe cone of symmetric positive definite matrices. Ourresult includes affine diffusion processes and thereforeextends considerably the known statements concern-ing Wishart processes.

Exponential (Geometric) Levy ProcessModels in Mathematical FinanceYoshio MIYAHARA (Graduate School of Eco-nomics, Nagoya City University)

The geometric Levy process (GLP) models playvery important roles in the field of mathematical fi-nance. These models are incomplete market models. Itis well-known that the distributions of the log returnsfrom the market data of the asset prices have the asym-metry and the fat tail. The GLP models have thoseproperties in general. Among them the geometric sta-ble process (GSP) model is probably the most impor-tant model. The importance of the stable process wasdiscussed by Fama(’63).

In the framework of arbitrage theory, the martingalemeasure is essential. The minimal entropy martingalemeasure (MEMM=CMM) was introduced by Miya-hara(’96). Combining the GLP and the MEMM we

obtain the [GLP & MEMM] pricing models (Miya-hara(’01)), and it is known that this model have manygood properties as an option pricing model for the in-complete market (Miyahara(’06)).

In this talk we shall overview the GLP option pric-ing models, and explain the properties of these mod-els. After that we shall see that the [GSP & MEMM]model has many advantages among the models for in-complete market. We also discuss several applicationsof GLP models to another problems in the mathemat-ical finance, for example the analysis of credit risk,optimal portfolio theory, etc.

[1] Fama, E. F. (1963), J. of Business, 36, 420-429.[2] Miyahara, Y. (1996), Proceedings of the Seventh

Japan-Russia Symposium, Tokyo 1995 (eds. S.Watanabe et al.), pp.343-352.

[3] Miyahara, Y. (2001), Asia-Pacific FinancialMarkets 8, No. 1, pp. 45-60.

[4] Miyahara, Y. (2006), Proceedings of the5th Ritsumeikan International Symposium‘ Stochastic Processes and Applications toMathematical Finance’ (eds. J. Akahori et al),pp. 125-156.

A Characterization of the MartingaleProperty of Exponentially Affine Pro-cessesJohannes MUHLE-KARBE (University of Vi-enna)

We consider local martingales of exponential formM = EX or exp(X) where X denotes one componentof a multivariate affine process in the sense of Duffie,Filipovic and Schachermayer (2003). By completingthe characterization of conservative affine processes in[Duffie et al. (2003), Section 9], we provide determin-istic necessary and sufficient conditions in terms of theparameters of X for M to be a true martingale.

Support theorem for SPDE and its appli-cation to HJM modelToshiyuki NAKAYAMA (Mitsubishi UFJ Mor-gan Stanley Securities Co., Ltd.)

A support theorem will be shown for the mild solu-tion of the SDE in a Hilbert space of the form

dX(t) = A X(t) dt + b(X(t)) dt + σ(X(t)) dB(t)

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where B(t) is a Hilbert space-valued Wiener processand A is an infinitesimal generator for C0-semigroupof bounded linear operators. This equation containsthe SPDE within HJM model in mathematical finance.By using this support theorem we can prove a viabilitytheorem, which is useful for “consistency problems”in interest rate models.

On the identification of hidden point-wise Holder exponentsQidi PENG (Paul Painleve laboratory, Lille 1 uni-versity)

Since several years, a number of authors have beeninterested in the statistical problem of the estimationof the poitwise Holder exponent (PHE) αX(t) startingfrom the observation of a discretized trajectory of theprocess X. However, it does not always seem to be re-alistic to assume that such an observation is availablebut only a corrupted version of it and a natural ques-tion one can address is that whether it is still possibleto estimate αX(t). More precisely we assume that thenon Gaussian process Z = Z(t)t∈[0,1] is the ”corruptedversion” of the multifractinal Brownian motion X, it isdefined as

Z(t) := z0 +

∫ t

0Φ(X(s))dW(s). (10)

The goal of our talk is to study the statistical prob-lem of the estimation of a hidden PHE in this new set-ting where this exponent has a rather complex struc-ture since it is allowed to evolve with time.

Cylindrical Levy processes in BanachspacesMarkus RIEDLE (University of Manchester)

Cylindrical Wiener processes are a well known andoften used source of random noise for models in in-finite dimensional spaces. We begin this talk withreviewing cylindrical Wiener processes by using theclassical theory of cylindrical processes and cylindri-cal measures. This approach enables us to definecylindrical Levy processes as a straightforward gen-eralisation of cylindrical Wiener processes.

In order to derive a Levy-Khintchine formula forcylindrical Levy processes we introduce the class of

infinitely divisible cylindrical measures and cylindri-cal Levy measures. In this context, we present someresults showing the close relations between probabil-ity theory and geometry of Banach spaces.

The cylindrical approach allows to define a stochas-tic integral with respect to a cylindrical Levy processwithout any geometric constraints on the underlyingBanach space. We use this integral to develop a theoryof cylindrical stochastic Cauchy problems and demon-strate its practicalness by presenting some basic factson the cylindrical Ornstein-Uhlenbeck process drivenby a cylindrical Levy process.

(part of this talk is based on joint work with D. Ap-plebaum)

Relation between stochastic integralsand the geometry of Banach spacesBarbara RUDIGER (Bergische UniversitatWuppertal Angewandte Mathematik)

Necessary and sufficient conditions for the exis-tence of Ito Integral in a Banach space with respectto compensated Poisson random measure (cPrm) arediscussed . Joint with V. Mandrekar we show that, forgeneral separable Banach spaces F, an inequality ofthe type resulting for M -type 2 Banach spaces withconstant depending on cPrm is necessary and sufficientfor the existence of Ito integral having second momentfinite. In addition, if the constant is independent ofcPrm for all non -random functions then the Banachspace is of type 2. The major technique used is PettisIntegral by Rosinski, Suchanecki and a Banach Stein-haus Theorem.

Hitting distributions of stable and re-lated processesMichal RYZNAR (Institute of Mathematics andComputer Science, Wroclaw University of Technol-ogy)

Some results concerning the distribution of the firsthitting time TC of a closed, usually compact set C,for a symmetric stable process in d-dimensional spacewill be presented. The asymptotics at infinity of thetail function Px(TC > t) of the hitting time are wellknown and were obtained by Port. We complement

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these results by providing very precise estimates of thetail function for the whole range of x and t. In the caseof the relativistic stable processes we are able to getsimilar results in the one-dimensional case togetherwith some precise estimates of the transition probabil-ities of the killed process (after hitting a compact set).It seems that even in the case of the Brownian mo-tion in two dimensions some estimates have not beenknown before.

Height Fluctuations of 1D KPZ equationTomohiro SASAMOTO (Department of Mathe-matics, Chiba University)

The one-dimensional KPZ equation is studied. Forthe narrow wedge initial condition, we provide a for-mula for the height distribution in a determinantalform. We also discuss some of its properties.

Infinite Products of Exponential Levy-driven OU ProcessesNarn-Rueih SHIEH (Department of Mathemat-ics, National Taiwan University)

In this talk, we report some correlation and stochas-tic analysis of an exponential process associated witha Levy-driven OU Process, for which Levy measurehas suitable exp decay. The motivation is from themultifractal burst phenomena in internet traffics. Wealso present some numerical simulations to discuss therange of multifractality. This talk is based on jointworks with V. Anh, N. Leonenko, and E. Taufer ( Adv.Appl. Probab. 2008, and Nonlinearity 2010 ).

This talk is presented at the Organized ContributedSession, Some Analysis related to Exponential (Geo-metric) Processes, 34th SPA at Osaka.

Generalized Feynman graphs represen-tation of stochastic differential equa-tions driven by Levy noiseBoubaker SMII (King Fahd University ofPetroleum and Minerals)

Stochastic differential equations driven by Levynoise are intensively studied. But so far there seemsto be no recipe to find out which kind of noise giventhe general structure of the equation. In fact this

can be obtained by recalling a graphical representa-tion of the solution of the SPDE driven by Levy noise.The graphs introduced are called generalized Feynmangraphs and a numerical value will be assigned to eachgraph. Our graphs formalism can be applied to dif-ferent stochastic differential equations as an examplea graphical representation of the solution of the LevyOrnstein–Uhlenbeck equation will be given as well inthis talk.

Sensitivity and hypoellipticity for jumpprocessesAtsushi TAKEUCHI (Department of Mathemat-ics, Osaka City University, JAPAN)

Fix T > 0. Let dν be the Levy measure over Rm\0,a0, a1, . . . , am ∈ C∞1+,b(Rd ; Rd), and b ∈ C∞,11+,b(Rd ×(Rm\0) ; Rd). For x ∈ Rd, consider the jump-typestochastic differential equation: x0 = x,

dxt = a0(xt) dt +m∑

i=1

ai(xt) dwit

+

∫|θ|≤1

b(xt−, θ) dJ +∫|θ|>1

b(xt−, θ) dJ,

where (w1t , . . . ,w

mt ) ; t ∈ [0,T ] is an m-dimensional

Brownian motion, dJ is a Poisson random measure on[0,T ] × (Rm\0) with the intensity dJ = dt dν, anddJ = dJ − dJ. It is well known that the Hormander–type condition on the coefficients, and the conditionon the Levy measure dν gurantee the existence of thesmooth density for xT with respect to the Lebesguemeasure on Rd, via the Malliavin calculus (cf. [2]).

In this talk, we shall study the sensitivity forthe solution xT in the initial point x ∈ Rd, un-der the Hormander–type condition on the coefficients.The martingale approach based upon the Kolmogorovbackward equation plays a crucial role in our study (cf.[3]). The Greeks computation for Asian option for as-set price dynamics is a typical example.

[1] E. Fournie, J. M. Lasry, J. Lebuchoux, P. L. Lions,N. Touzi, Applications of Malliavin calculus toMonte–Carlo methods in finance, Finance Stoch.,3, 391–412 (1999).

[2] T. Komatsu, A. Takeuchi, On the smoothness ofpdf of solution to SDE of jump type, Int. J. Diff.Eqns. Appl., 2, 141–197 (2001).

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[3] A. Takeuchi, The Bismut–Elworthy–Li-typeformulae for stochastic differential equations withjumps, J. Theor. Probab., 23, 576–604 (2010).

Complex Brownian Motion Representa-tion for the Dyson ModelHideki TANEMURA (Department of Mathemat-ics and Informaics, Chiba University)

Dyson introduced a one-dimensional system ofBrownian motions with long-range repulsive forcesacting between any pair of particles. We considerthe case that the strength of the two-body repulsiveforce is exactly equal to the inverse of particle dis-tance, and call the system in this case the Dyson modelin the present talk. For a given initial configurationξ, we show that the moment generating function fortwo-time distribution of the Dyson model is expressedby independent complex Brownian motions (CBMs)starting from the points on the real axis in suppξ =x ∈ R : ξ(x) > 0. The CBM representation canbe regarded as an extension of h-transformation to theformula, which is valid also for infinite particle sys-tems. Using this representation we derive that the pro-cess is determinantal in the sense that the moment gen-erating function of any multitime distribution is givenby a Fredholm determinant associated with a continu-ous kernel. We also prove the tightness of a series ofprocesses, which converges to the Dyson model withan infinite number of particles.

Invariant manifolds with boundary forjump-diffusionsStefan TAPPE (ETH Zurich)

We give necessary and sufficient conditions forstochastic invariance of finite dimensional subman-ifolds with boundary for stochastic partial differen-tial equations driven by Wiener processes and Poissonmeasures. Due to the boundary of the submanifold, wealso investigate stochastic invariance of (curved) halfspaces for finite dimensional jump-diffusions. Fur-thermore, we provide several examples illustrating ourresults.

Pricing swing options by a dual ap-proachYusuke TASHIRO (Tokyo University)

We discuss a dual approach for pricing swing op-tions with typical constraints, such as daily and annualconstraints. It is known that the pricing problem ofthe swing option is defined as a multiple optimal stop-ping problem. In this paper, we analyze the optimalexercise strategy of the swing option and show thatthe strategy satisfies some kind of monotonicity. Us-ing this monotonicity, we show that the multiple stop-ping problem is decomposed into single optimal stop-ping problems under some conditions, and then we cancompute the price of the swing options by solving thesingle stopping problems.

Applications of spectral methods forquantum random walksLuis VELAZQUEZ (Departamento deMatematica Aplicada, Universidad de Zaragoza)

This talk will show some of the advantages ofthe spectral approach for one-dimensional quantumwalks. In particular, we will see how recurrence andlocalization properties of a quantum walk are codifiedin this approach. A detailed analysis of some exampleswill illustrate the effectiveness of the method. This isa joint work with A. F. Grunbaum (University of Cal-ifornia, Berkeley), M. J. Cantero and L. Moral (Uni-versidad de Zaragoza, Spain).

Distributional analysis of a generaliza-tion of the Polya processGordon WILLMOT (Statistics and Actuarial Sci-ence, University of Waterloo)

A nonhomogeneous birth process generalizing thePolya process is analyzed, and the distribution of thetransition probabilities is shown to be the convolu-tion of a negative binomial distribution and a com-pound Poisson distribution whose secondary distribu-tion is a mixture of zero-truncated geometric distri-butions. Simplification of the form of the secondarydistribution is obtained when the transition intensitieshave a particular structure, and may sometimes be ex-pressed in terms of Stirling numbers and special func-tions such as the incomplete gamma function, the in-complete beta function, and the exponential integral.Conditions under which the compound Poisson formof the marginal distributions may be improved to a ge-ometric mixture are also given.

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Refinements of the two-sided boundsfor renewal equationsJae-Kyung WOO (Statistics and Actuarial Sci-ence, University of Waterloo)

Many quantities of interest in the study of renewalprocesses may be expressed as a special type of inte-gral equation known as a renewal equation. The mainpurpose of this talk is to provide bounds for a solutionof renewal equations based on various reliability clas-sifications. It contains exponential and nonexponen-tial types of inequalities for renewal equations. In par-ticular, the two-sides bounds with specific reliabilityconditions become sharp which are equivalent to theexact solution. Finally, some examples involving theultimate ruin for the classical Poisson model includingtime-dependent claim sizes case, the joint distributionof the surplus prior to ruin and at ruin, and the excesslife time are provided.

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Open Contributed SessionsAn Algebraic Approach to the Cameron-Martin-Maruyama-Girsanov formulaTakafumi AMABA (Department of MathematicalSciences, Ritsumeikan University)

In this talk, we will give a new perspective tothe Cameron-Martin-Maruyama-Girsanov formula bygiving a totally algebraic proof to it. It is based onthe exponentiation of the Malliavin-type differentia-tion and its adjointness.

Card counting in continuous timePatrik ANDERSSON (Stockholm University)

In some casino card games, like Blackjack, it ispossible to turn a subfair game in to a superfair forthe player. This is possible since several coups areplayed before reshuffling and the composition of thedeck may therefore change so that at times the ex-pected value of the game is positive. Card countingis the technique of using a linear estimator of the ex-pected value to find these advantageous situations andbet accordingly. We treat the case of a large numberof decks and find an SDE that approximates the profitsfrom the game. We also find the Kelly optimal strategyand show that this is a natural extension of the resultsfrom the case with a finite number of decks.

Convex risk measures on Orlicz spaces:inf-convolution and shortfallTakuji ARAI (Keio University)

We focus on, throughout this paper, convex riskmeasures defined on Orlicz spaces. In particular,we investigate basic properties of inf-convolutions de-fined between a convex risk measure and a convex set,and between two convex risk measures. Moreover,we study shortfall risk measures, which are convexrisk measures induced by the shortfall risk. By us-ing results on inf-convolutions, we obtain a robust rep-resentation result for shortfall risk measures definedon Orlicz spaces under the assumption that the set ofhedging strategies has the sequential compactness in aweak sense. We discuss in addition a construction ofan example having the sequential compactness.

Parameter-dependent optimal stoppingproblems for one-dimensional diffu-sionsChristoph BAUMGARTEN (Technische Uni-versitat Berlin)

We consider a class of optimal stopping problemsfor a linear diffusion whose payoff depends on a linearparameter. Problems of this type may allow for a uni-versal stopping signal that characterizes optimal stop-ping times for any given parameter via a level-crossingprinciple for some auxiliary process.

For linear diffusions, we provide an explicit con-struction of this signal in terms of the Laplace trans-form of level passage times. Explicit solutions areavailable under certain concavity conditions on the re-ward function. In general, the construction of the sig-nal at a given point reduces to finding the infimum ofan auxiliary function of one real variable. Moreover,we show that monotonicity of the stopping signal cor-responds to monotone and concave (in a suitably gen-eralized sense) reward functions. As an application,we consider American put options as well as the com-putation of Gittins indices for optimal allocation prob-lems.

This talk is based on joint work with Peter Bank(Technische Universitat Berlin).

On the central limit theorem for trimmedr.v.’sIstvan BERKES (Graz University of Technology,Institute of Statistics)

Asymptotic properties of trimmed i.i.d. sequencesplay an important role in probability and statistics andhave been studied widely in the literature. One openproblem of the theory is the central limit theorem formodulus trimmed sums which exhibits a number ofpathological phenomena and is understood only in thecase of symmetric r.v.’s. We prove that for i.i.d. se-quences in the domain of attraction of a stable law, themodulus trimmed sums always satisfy the CLT witha suitable random centering factor and we give fairlyprecise criteria for the ordinary CLT to hold. We give

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applications of our results to change point tests forvariables with infinite variance.

Spatial random permutations andPoisson-Dirichlet distributionVolker BETZ (Mathematics Institute, Universityof Warwick)

Spatial random permutations act on a set with spa-tial structure. The probability of obtaining a givenpermutation is determined by a Gibbs factor, and theenergy is higher when the permutation contains morejumps between distant points of the underlying set. So,the typical jump length of a random spatial permuta-tion will be finite.

For this model there is a phase transition in the ther-modynamic limit; the order parameter is the density ofthe points forming the spatial structure. Only cycles offinite length appear for low density, while above an ex-plicit critical density there is coexistence of finite andmacroscopic cycles. The length of the macroscopiccycles is distributed according to a Poisson-Dirichletlaw.

This is joint work with Daniel Ueltschi.

On the mixture of the displaced expo-nential distribution and the uniform dis-tributionEpimaco, Jr. Alamares CABANLIT (Min-danao State University, General Santos City)

The Displaced Exponential Distribution is a goodmodel for traffic flow and in survival analysis. How-ever, there are some instances where realities wouldnot fit this model due to some contamination and irreg-ularities. In this case, we consider the Uniform Distri-bution as one of the contaminants. This paper deals onthe mixture of the Displaced Exponential and the Uni-form Distribution. In this paper we give the importantsummaries of the mixture. We estimate the param-eters by using the Maximum Likelihood Estimation.Graphs of the distribution are exhibited.

Keywords and Phrases: Displaced Exponential Dis-tribution, Uniform Distribution, Moment Generat-ing Function, Characteristic Function and MaximumLikelihood Estimation.

AMS Classification No. 60E05, 60E10, 62H15

Interararrival time distribution for a non-Markovian arrival processMine CAGLAR (Koc University)

We consider a workload input process which cap-tures the dynamics of packet generation in data traffic.For t ∈ R+, it is constructed as

Y(t) =∫R

∫R+

∫E

N(ds, dr, du) [u(r∧(t−s))−u(r∧(−s))]

by a Poisson random measure N governing the sessionarrival time S and duration R, and the packet genera-tion process U over each session, where E is the spaceof cadlag functions on R+ [1]. The process Y accountsfor long-range dependence and self-similarity exhib-ited by real traces through the mean measure of N.

The distribution of the interarrival times is of inter-est in a queuing system receiving the non-Markovianinput Y . We exploit a compound Poisson processfor packet generation to find the probability law ofthe packet interarrivals. The model is appropriate foranalytical results on queuing performance with self-similar input in contrast to its limiting forms, namelyfractional Brownian motion and Levy process.[1] M. Caglar (2004) A Long-Range Dependent

Workload Model for Packet Data Traffic, Math.OR, 29: 92-105.

Existence and Uniqueness of RandomGradient StatesCodina COTAR (Technische UniversitaetMuenchen)

We consider statistical mechanics models of contin-uous spins in a disordered environment. These mod-els have a natural interpretation as effective interfacemodels. It is well known that without disorder thereare no interface Gibbs measures in infinite volume indimension d = 2, while there are gradient Gibbs mea-sures describing an infinite-volume distribution for theincrements of the field, as was shown by Funaki andSpohn. It was also shown by van Enter and Kulske thatadding a disorder term prohibits the existence of suchgradient Gibbs measures for general interaction poten-tials in d = 2. We present in this talk some new resultsof existence and uniqueness of shift-covariant, gradi-ent Gibbs measures, obtained for gradient interactionswith strictly convex potential and with disorder term inthe Hamiltonian. (Based on joint work C. Kuelske).

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A model for multiscaling and clusteringof volatility in financial indexesPaolo DAI PRA (Universita di Padova)

Recent developments in stochastic modelling oftime series have been strongly influenced by the anal-ysis of financial indexes. The basic model, that hasgiven rise to the celebrated Black & Scholes formula,assumes that the logarithm Xt of the price of the un-derlying index, after subtracting the trend, is given by

dXt = σ dWt,

where σ (the volatility) is a constant and (Wt)t≥0 is astandard Brownian motion.

Despite its success, this model is not consistent witha number of stylized facts that are empirically detectedin many real time series. Some of these facts are thefollowing:

• the volatility is not constant; in particular it mayhave high peaks, that can be interpreted as shocksin the market;

• the empirical distribution of the increments Xt+h−Xt of the logarithm of the price (the log-returns)has tails heavier than Gaussian;

• log-returns corresponding to disjoint time-interval are uncorrelated, but not independent: infact, the correlation between the absolute values|Xt+h − Xt | and |Xs+h − Xs| has a slow decay in|t − s|, up to moderate values for |t − s|. This phe-nomenon is known as clustering of volatility.

We propose a continuous-time stochastic modelwhich, on the one hand, captures the above stylizedfact and, on the other hand, is easy to describe, in-terpret and simulate. In particular it can be used forapplications such as option pricing.

Optimal control of trading algorithms: ageneral impulse control approachNgoc-Minh DANG (CEREMADE, UniversityParis Dauphine)

We propose a general framework for intra-day trad-ing based on the control of trading algorithms. Given ageneric parameterized algorithm, we control the dates

(τi)i at which it is launched, the length (δi)i of the trad-ing period and the value of the parameters (Ei)i keptduring the time interval [τi, τi + δi[. This gives riseto a non-classical impulse control problem where notonly the regime Ei but also the period [τi, τi+δi[ has tobe determined by the controller at the impulse time τi.We adapt the weak dynamic programming principle ofBouchard and Touzi (2009) to our context and providea characterization of the associated value function as adiscontinuous viscosity solution of a system of PDEswith appropriate boundary conditions, for which weprove a comparison principle. We also propose a nu-merical scheme for the resolution of the above systemand show that it is convergent. We finally provide anexample of application to a problem of optimal stocktrading with a non-linear market impact function.

On the Strong solution for the stochas-tic 3D Leray-alpha model of turbulenceGabriel DEUGOUE (University of Pretoria-South Africa)

In this talk, we prove the existence and uniquenessof strong solution to the stochastic 3D Leray-α equa-tions under appropriate conditions on the data. Thisis achieved by means of the Galerkin approximationscombines with the weak convergence methods. Wealso study the asymptotic behavior of the strong solu-tion as alpha goes to zero. We show that a sequenceof strong solution converges in appropriate topolo-gies to weak solutions of the stochastic 3D Navier-Stokes equations. The result has been the object ofpublications in Journal BOUNDARY VALUE PROB-LEMS(2010)

Infinite dimensional calculus via regu-larization with financial motivationsCristina DI GIROLAMI (University LUISSGuido Carli)

This talk develops some aspects of stochastic calcu-lus via regularization to Banach valued processes. Anoriginal concept of χ-quadratic variation is introduced,where χ is a subspace of the dual of a tensor productB⊗B where B is the values space of the process. Partic-ular interest is devoted to the case when B is the spaceof real continuous functions defined on [−τ, 0], τ > 0.Ito formulae and stability of finite χ-quadratic varia-

78

tion processes are established. Attention is devoted toa finite real quadratic variation (for instance Dirichlet,weak Dirichlet) process X. The C([−τ, 0])-valued pro-cess X(·) defined by Xt(y) = Xt+y where y ∈ [−τ, 0],is called window process. Let T > 0. If X is a finitequadratic variation process such that [X]t = t and h =H(XT (·)) where H : C([−T, 0]) −→ R is L2([−T, 0])-smooth or H non smooth but finitely based it is possi-ble to represent h as a sum of a real H0 plus a forwardintegral of type

∫ T0 ξd−X where H0 and ξ are explicitly

given. This representation result will be strictly linkedwith a function u : [0,T ]×C([−T, 0]) −→ R solving aninfinite dimensional partial differential equation withthe property H0 = u(0, X0(·)), ξt = Dδ0 u(t, Xt(·)) :=Du(t, Xt(·))(0). This decomposition generalizes theClark-Ocone formula which is true when X is the stan-dard Brownian motion W. The financial perspective ofthis work is related to hedging theory of path depen-dent options without semimartingales.

Joint work with Francesco RUSSO

[1] Di Girolami C. and Russo F. Infinite dimensionalstochastic calculus via regularization andapplications available at HAL-INRIA, Preprint;http://hal.archives-ouvertes.fr/inria-00473947/fr/

[2] Di Girolami C. and Russo F. Clark-Ocone typeformula for non-semimartingales with non-trivialquadratic variation available at HAL-INRIA,Preprint; http://hal.archives-ouvertes.fr/inria-00484993/fr/

The on-off network traffic model underintermediate scalingClement DOMBRY (Universite de Poitiers, Lab-oratoire de Mathematiques et Applications)

In this work in collaboration with I.Kaj, we pro-vide a new result that helps completing a unified pic-ture of the scaling behavior in heavy-tailed stochasticmodels for transmission of packet traffic on high-speedcommunication links. Popular models include infinitesource Poisson models, models based on aggregatedrenewal sequences, and models built from aggregatedon-off sources. The versions of these models with fi-nite variance transmission rate share the following pat-tern: if the sources connect at a fast rate over time the

cumulative statistical fluctuations are fractional Brow-nian motion, if the connection rate is slow the traf-fic fluctuations are described by a stable Levy pro-cess, while the limiting fluctuations for the interme-diate scaling regime are given by fractional Poissonmotion. Here we focus on the intermediate scaling forthe on-off model.

On the Cauchy problem for degeneratebackward stochastic partial differentialequations in Sobolev spacesKai DU (Department of Finance and Control Sci-ences, School of Mathematical Sciences, Fudan Uni-versity)

In this talk, we study degenerate parabolicbackward stochastic partial differential equations(BSPDEs) inRd. We first establish a Wm,p-estimate forthe adapted solutions to BSPDEs in a general setting.Based on this estimate, the existence and uniquenessresults are obtained in Sobolev spaces. Moreover, un-der the assumption that mp > d, a connection betweenthe solutions of BSPDEs and the solutions of FBSDEsis established by the approximation method.

On stochastic Burgers PDEs with ran-dom coefficients and a generalization ofthe Cole-Hopf transformationNikolaos ENGLEZOS (Department of Bankingand Financial Management, University of Piraeus)

Burgers equation is a quisilinear partial differentialequation, proposed in 1930’s to model the evolutionof turbulent fluid motion, which can be linearized tothe heat equation via the celebrated Cole-Hopf trans-formation. This paper introduces and studies in detailgeneral versions of stochastic Burgers equation withrandom coefficients, in both forward and backwardsense. Concerning the former, the Cole-Hopf transfor-mation still applies and we reduce a forward stochasticBurgers equation to a forward stochastic heat equationthat can be treated in a “pathwise” manner. In caseof deterministic coefficients, we obtain a probabilis-tic representation of the Cole-Hopf transformation byassociating the backward Burgers equation with a sys-tem of forward-backward stochastic differential equa-tions. Returning to random coefficients, we exploitthis representation in order to establish a stochastic

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version of the Cole-Hopf transformation. This ex-tended transformation allows us to find solutions to abackward stochastic Burgers equation through a back-ward stochastic heat equation, subject to an additionalequation that reflects the presence of randomness inthe coefficients. In both settings, forward and back-ward, stochastic Feynman-Kac formulae are derivedfor the solutions of the respective stochastic Burgersequations, as well. Finally, applications that illus-trate the obtained results in the forward and backwardframework are presented to a controllability problemand to a pricing/hedging problem arising from mathe-matical finance, respectively.

Stochastic expansion for the pricing ofcall options with discrete dividendsPierre ETORE (LJK - ENSIMAG)

We consider a complete financial market, with arisky asset of price (S y,δ

t )t, on which an European Callvanilla option with maturity T and strike K is written(we denote P its price). At known dates 0 < t1 < . . . <tn ≤ T the asset pays dividends of the form

δi + yiSy,δti−.

Between two dividend payment dates the asset followsa Black and Scholes dynamic (BSD) with parametersσ and r.

An easy induction shows that

S y,δT = π0,nS T −

n∑i=1

δiπi,nS T

S ti,

where πi,n := Πnj=i+1(1− y j) and (S t)t denotes the price

of an asset following the BSD with parameters σ andr (but with no discrete dividends).

We aim at writing an expansion

P = P0 + correction terms + error,

using a suitable proxy (we work for instead in the spiritof Smart expansion and fast calibration for jump dif-fusion by E. Benhamou, E. Gobet, M. Miri, Financeand Stochastics, Vol. 13(4), pp.563-589, 2009). Wewill have

P0 = E[e−rT (π0,nS T − Ky,δ)+],

with Ky,δ a transformation of K depending on (y, δ).Indeed we can easily compute this leading term us-ing the Black-Scholes formula. The correction terms

appears as Greeks of the Call option, multiplied byexplicit coefficients, and can be computed explicitely.We analyse the error in our expansion using Malliavincalculus.

Finally, numerical experiments show the accuracyof our method, up to less than one b.p. error on im-plied volatilies.

Discretization error in stochastic inte-grationMasaaki FUKASAWA (Osaka University)

Limit distributions for the error in approximationsof stochastic integrals by Riemann sums with stochas-tic partitions are studied. The integrands and integra-tors are supposed to be one-dimensional continuoussemimartingales. Lower bounds for asymptotic con-ditional variance of the error are given and effectivediscretization schemes which attain the lower boundsare constructed. Two examples of thier applicationsare given; efficient delta hedging strategies under fixedor linear transaction costs, and effective discretizationschemes for the Euler-Maruyama approximation areconstructed.

Brownian motion among heavy tailedPoissonian potentialRyoki FUKUSHIMA (Tokyo Institute of Tech-nology)

We consider the Feynman-Kac functional associ-ated with a Brownian motion among a random po-tential. The potential is defined by attaching a heavytailed positive potential around the Poisson point pro-cess. This model was first considered by Pastur [1]and the first order term of the moment asymptotics wasdetermined. We determined both moment and almostsure asymptotics of the Feynman-Kac functional up tothe second order. These higher order terms give in-formation about the behavior of the Brownian motionconditioned to avoid the potential.

[1] L. A. Pastur. The behavior of certain Wienerintegrals as t → ∞ and the density of states ofSchrodinger equations with random potential.Teoret. Mat. Fiz., 32(1):88–95, 1977.

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Lp-approximations of stochastic inte-grals and weighted BMOStefan GEISS (University of Innsbruck, Instituteof Mathematics)

We study the error in Riemann discretizations ofstochastic integrals driven by X = (Xt)t∈[0,1], which iseither the Brownian motion or the geometric Brownianmotion. Given f (X1) ∈ L2 and a time-net τ = (ti)n

i=0,we consider

f (X1) = E f (X1) +∫ 1

0LtdWt

∼ E f (X1) +n∑

k=1

Ltk−1

(Xtk − Xtk−1

)with the corresponding error process

Ct( f , τ) :=∫ t

0LsdXs −

n∑k=1

Ltk−1

(Xtk∧t − Xtk−1∧t

).

We investigate the Lp-error ‖C1( f , τ)‖p for 2 < p < ∞and the limiting case p = ∞ by ‖C( f , τ)‖BMO2(φ), whereBMO2(Φ) is an appropriate weighted BMO-space. Wepresent results where the behavior of ‖C1( f , τ)‖p isrelated to (and also characterized by) the fractionalsmoothness of f (X1) in terms of the Malliavin Besovspaces Bθp,∞ = (Lp,D1,p)θ,∞ obtained by real inter-polation. The case p = ∞ generalizes results from(S. Geiss: Weighted BMO and discrete time hedgingwithin the Black-Scholes model. Probab. Th. Rel.Fields. 132(2005)).

The graph-value Random variable andthe unique existence of probabilisticmeasurementXianmin GENG (Nanjing University of Aeronau-tics and Astronautics)

There are a large number of graph-value stochas-tic processes in the real world, and the theory ofgraph value stochastic processes appeared insuffi-ciency. This paper researches the property of thegraph-value functions and graph-value random vari-able, establishes the probability space where fit graph-value stochastic process, and obtains the condition thatthe probabilistic measurement exists only

Constrained portfolio choices in the de-cumulation phase of a pension planFausto GOZZI (Luiss University)

This paper deals with a constrained investmentproblem for a defined contribution (DC) pension fundwhere retirees are allowed to defer the purchase of theannuity at some future time after retirement.

This problem has already been treated in the uncon-strained case in a number of papers. The aim of thiswork is to deal with the more realistic case when con-straints on the investment strategies and on the statevariable are present. Due to the difficulty of the task,we consider the basic model of [GerHabVig04], whereinterim consumption and annuitization time are fixed.The main goal is to find the optimal portfolio choiceto be adopted by the retiree from retirement to annu-itization time in a Black and Scholes financial market.We define and study the problem at two different com-plexity levels. In the first level (problem P1), we onlyrequire no short-selling. In the second level (problemP2), we add a constraint on the state variable, by im-posing that the final fund cannot be lower than a cer-tain guaranteed safety level. This implies, in particu-lar, no ruin.

The mathematical problem is naturally formulatedas a stochastic control problem with constraints on thecontrol and the state variable, and is approached by thedynamic programming method. We give a general re-sult of existence and uniqueness of regular solutionsfor the Hamilton-Jacobi-Bellman equation and, in aspecial case, we explicitly compute the value functionfor the problem and give the optimal strategy in feed-back form.

A numerical application of the special case – whenexplicit solutions are available – ends the paper andshows the extent of applicability of the model to a DCpension fund in the decumulation phase.

Weak Law for Number of Edges on aSpherical SurfaceBhupendra GUPTA (Indian Institute of In-formation Technology -Desigm and Manufacturing-Jabalpur)

In this article, we consider ‘N’spherical caps of area4πp were uniformly distributed over the surface of aunit sphere. We study the random intersection graphGN constructed by these caps. We prove that for

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p = cNα , c > 0 and α > 2, the number of edges in

graph GN follow the Poisson distribution.

Volatility in the Black-Scholes and otherformulaeKais HAMZA (Monash University)

The Black-Scholes formula has been derived underthe assumption of constant volatility in stocks. In spiteof evidence that this parameter is not constant, thisformula is widely used by the markets. This paper ad-dresses the question of whether a model for stock priceexists such that the Black-Scholes and similar formu-lae hold for other models. We consider the case of acontinuum of strikes as well as that of finitely manystrikes.

Joint work with Fima Klebaner and Olivia Mah

Ergodicity and density asymptoticsof complex diffusion processes withquadratic driftDavid Paul HERZOG (The University of Arizona,Department of Mathematics)

We study a family of complex diffusion processeswith quadratic drift. The particular family of stochas-tic differential equations we consider models the rel-ative motion of two particles suspended in an incom-pressible fluid flow. We will outline a proof that theseprocesses are absent of explosions and possess uniqueinvariant probability measures. We will note that theinvariant probability densities have power law decayat infinity, and also highlight useful techniques in thestudy of such processes.

On the Robustness of the Snell enve-lope applied to the analysis of variousapproximation schemesPeng HU (INRIA - University Bordeaux 1)

We analyze the robustness properties of the Snellenvelope backward evolution equation for discretetime models. We provide a general robustness lemma,and we apply this result to a series of approximationmethods, including cut-off type approximations, Eulerdiscretization schemes, interpolation models, quanti-zation tree models, and the Stochastic Mesh method

of Broadie-Glasserman. In each situation, we pro-vide non asymptotic convergence estimates, includingLp-mean error bounds and exponential concentrationinequalities. In particular, this analysis allows us torecover existing convergence results for the quantiza-tion tree method and to improve significantly the ratesof convergence obtained for the Stochastic Mesh es-timator of Broadie-Glasserman. In the final part ofthe article, we propose a genealogical tree based al-gorithm based on a mean field approximation of thereference Markov process in terms of a neutral typegenetic model. In contrast to Broadie-GlassermanMonte Carlo models, the computational cost of thisnew stochastic particle approximation is linear in thenumber of sampled points.

Fair allocation via optimal transporta-tionMartin Otto Josef HUESMANN (Universityof Bonn)

An optimal transportation map minimises the inte-gral over a given cost function among all couplings oftwo given probability measures.A fair allocation between Lebesgue measure and aPoisson random measure on Rd is a (random) map thatassigns to each point in the support of a realisation ofthe Poisson measure a set of Lebesgue measure one.By using optimal transport theory with cost functionc(x, y) = |x − y|p, p ≥ 1, we construct a coupling ofLebesgue measure and Poisson measure. This cou-pling, which is a fair allocation, has finite cost per unitif d > 2. It can also be thought of as an optimal trans-portation map between Lebesgue measure and a Pois-son random measure.

(joint work with K.-T. Sturm)

Profile Monitoring via Penalized SplineRegressionLongcheen HUWANG (National Tsing Hua Uni-versity)

In this talk, a penalized spline regression modelis used to describe the complex relationship (pro-file) between a response variable and an explanatoryvariable. By treating the penalized spline regressionmodel as a general linear mixed model, we can esti-

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mate the parameters of the penalized spline regressionmodel by the technique for fitting the general linearmixed model. A Shewhart-type simultaneous confi-dence band (SCB) chart built by the penalized splineregression model is proposed to monitor the profilesin the Phase II anlysis. Simulation studies are con-ducted to evaluate the performance of the SCB chart.An example used to demonstrate the applicability ofthe proposed chart is provided as well.

On collisions of Brownian particlesTomoyuki ICHIBA (Department of Statistics andApplied Probability University of California, SantaBarbara)

We examine the behavior of n Brownian particlesdiffusing on the real line with bounded, measurabledrift and bounded, piecewise continuous diffusion co-efficients that depend on the current configuration ofparticles. Sufficient conditions are established forthe absence, and for the presence, of triple collisionsamong the particles. As an application to the Atlasmodel for equity markets, we study local times in thedynamics of ranked continuous semimartingales and aspecial construction of such systems of diffusing par-ticles using Brownian motions with reflection on poly-hedral domains.

Large time behavior of solutions ofHamilton-Jacobi-Bellman equationswith quadratic nonlinearity in gradientsNaoyuki ICHIHARA (Graduate School of Engi-neering, Hiroshima University)

We are concerned with the large time behaviorof solutions to the Cauchy problem for semi-linearparabolic equations having quadratic nonlinearity ingradients. Equations of this kind often appear instochastic control theory. It turns out that as time tendsto infinity the solution of the Cauchy problem con-verges to a function of variable separation type char-acterized by the so-called ergodic type Bellman equa-tion.

On the joint distribution of two quantilesYuri IMAMURA (Ritsumeikan University)

Let (Xt, t ≥ 0) be a stochastic process. We definethe α-quantile of Xs (0 ≤ s ≤ t) by M(α, t) = infx :∫ t

0 1(Xs≤x)ds > αt. When X is a Levy process, it holdsthat M(α, t) = sup0≤s≤αt X(s) + inf0≤s≤(1−αt) X′(s) inlaw, where X′ is an independent copy of X. This isproved by Dassios [1] based on the results by Wendel[3] and Port [3].

In this talk, I will discuss a generalization of theDassios-Wendel-Port formla where the joint distribu-tion of M(α, t) and M(β, t) is concerned.[1] Dassios, A.,Sample quantiles of stochastic

processes with stationary and independentincrements, Ann. Appl. Probab., 6, 1041-1043.,1996.

[2] Port, S. C., An elementary probability approachto fluctuation theory. J.Math. Anal., 1963. Appl. 6109-151.

[3] Wendel, J.G., Order statistics of partial sums.Ann. Math. Statist., 31, 1034-1044, 1960.

Composition with distributions ofWiener-Poisson variables and itsasymptotic expansionYasushi ISHIKAWA (Dept. Math., Ehime Uni-versity)

Asymptotic expansion with respect to a small pa-rameter is considered for jump-diffusion processes onthe Wiener-Poisson space. We first introduce Sobolevspaces over the Wiener-Poisson space by using thederivative and the difference operators. We then de-fine the composition of the random variables with ele-ments in the distributions. This leads to the asymptoticexpansion. (joint work with Masafumi Hayashi)

Extended Random Signal-to-Interference-and-Noise-Ratio Graphs with FadingSrikanth Krishnan IYER (Indian Institute ofScience Bangalore)

We study the asymptotic properties of a random ge-ometric graph (SINR-F) on uniform points in which adirected link exists between two nodes if the signal tointerference-noise ratio is above a certain threshold.

We first study such a graph in the presence of fad-ing effects alone (RGG-F). For this graph we prove analmost sure limit for the critical power required to en-sure that the graph does not possess isolated nodes and

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a criterion under which the number of isolated nodesconverges in distribution to a Poisson distribution. Wederive a sufficient condition under which the graphwill be connected with high probability and derive al-most sure bounds on the maximum and minimum ver-tex degrees.

We then prove an almost sure upper bound onthe maximum received interfence. This allows us tochoose an asymptotic spread parameter so as to boundthe maximum received interference. With this choiceof spread parameters we can extend the results ob-tained for RGG-F to SINR-F.

Fault-Detecting Time Evaluations byDiscrete Stochastic Models on SoftwareFault-Failure ProcessesShuen-Lin JENG (Dept. of Statistics, NationalCheng Kung University)

Many software reliability growth models (SRGMs)have been developed for the nonhomogeneous Poissonprocesses (NHPP). The situation considered in most ofthese models is for the case that the failure event is in-duced by only one fault of the software system. Inpractice, however, a failure event may be caused bytwo or more faults. To resolve this issue, our workconsiders a more general model, i.e., a nonhomoge-neous discrete-compound Poisson (NHDCP) model,in the application on the software fault-failure pro-cesses (SFFPs).

In the paper by Jeske et al. (2005), the data werecollected through aggregated records of fault countsof all software systems in a test. Here we argue thatthe separated records of fault counts of each system ina SFFP are more informative for the inference of thefault-detecting time. The demonstration is providedby a simulation study. We show that not only the es-timates of fault-detecting time will be more accuratebut also the different failure modes can be indentifiedwhen data are collected through separated recording ina test of multiple systems.

A re-sampling algorithm to determinebest stopping criterion and Variable Se-lection in Cox’s Proportional HazardModelSalahuddin KAHN (University of Peshawar)

One of the common interests for model selectionin survival analysis is to determine a small numberof important risk factors called covariates. The chisquare test is based on the fixed level of stopping cri-terion in automated model selection methods. This isan essential step in order to assess all risk factors inmedical and public health studies. We propose an al-gorithm to choose best stopping criterion (values) forentry and removal of covariates in stepwise Cox’s pro-portion hazard model for each individual data set. Per-formance of model selected is evaluated on the basisof cross-validated partial log-likelihood used as a mea-sure of predictive value of the Cox’s proportion haz-ard model. The simulation and the boosted screen-ing study shows that our method is capable of findingbest stopping criterion and thereafter finding the cor-rect subset of covariates for regression model in sur-vival analysis. We illustrate our study with a real dataset conducted by Mayo Clinic.

Convergence of Markov measure valuedrandom variables and its application toMCMCKengo KAMATANI (University of Tokyo)

In this talk we address some asymptotic propertiesof P(DS [0,∞))-valued random variables, which ex-tend the results in Kamatani (2010 submitted). Weintroduce the notion of the consistency and the de-generacy for a sequence of P(DS [0,∞))-valued ran-dom variables. Some sufficient conditions for theseproperties are addressed. The main objective of thiswork is to describe bad behaviors of the Markov chainMonte Calro (MCMC) method, in particular, of theGibbs sampler. Under a set of regularity conditions,Kamatani (2010) showed that a sequence of the Gibbssampler tends to an AR process type random vari-able. On the other hand, with non-regularity, some-times a sequence of MCMC is degenerate in the limit,which may occur even if the transition kernels areuniformly ergodic. Moreover with time scaling (ex.t 7→ n−1/2t), it tends in distribution to a non-degenerateP(DS [0,∞))-valued random variables. These studiesprovide useful insight into the problem of how to con-struct efficient algorithms.

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The multiple scaling approximation in aheat shock model of E.coliHyeWon KANG (University of Minnesota)

Applying a multiple scaling method for chemicalreaction networks introduced in the paper by Kang andKurtz, we analyze a heat shock model of E.coli de-veloped by Srivastava, Peterson, and Bentley. We usea continuous-time Markov jump process to describestates of the chemical reaction network. Using balanceconditions, we systematically find an appropriate scal-ing for the number of molecules of chemical speciesand for chemical reaction rate constants both of whichvary over several orders of magnitude. After scalingand limiting, the complicated system is approximatedby several reduced systems constituted by processeswith the same time scale exponent. The reduced sys-tems are analytically more tractable and cost less com-putational load for simulation.

Operational Risk Measure in BayesiancontextMarie KRATZ (ESSEC Business School)

Some literature has been recently devoted to the useof a Bayesian inference approach in the context ofoperational risk. Many financial institutions adopt aLoss Distribution approach to estimate the risk capitalcharge, in order to meet the regulation requirements.Such approach requires combination of internal andexternal data, as well as expert opinions. In a recentwork, Lambrigger et al. introduced a Bayesian infer-ence model combining those three sources simultane-ously and setting the prior distribution on the marketrisk profile (external source). We aim at generaliz-ing this approach to propose a model closer to real-ity. To do so, we introduce an unknown parameterhaving a prior distribution on which each source willdepend. In doing so, we are in a pure Bayesian frame-work; it allows to consider also non-informative priordistributions, if no reliable information is available,and to increase the quantity of information (numberof sources) when computing the posterior distribution.It helps then to have more flexibility in the model. Thesecond way to generalize the model will be to relaxsome strong hypothesis such as the conditional inde-pendence of two of the three actors given the thirdone.Also, when adopting the Bayesian approach, wewant to propose an a priori distribution on a parame-

ter other than the market risk profile and to see whatdoes make more sense in practice when comparing thevarious modelling.

The equivalence of stochastic differen-tial equations and martingale problemsThomas G KURTZ (University of Wisconsin-Madison)

Stochastic ordinary and partial differential equa-tions driven by space-time Gaussian white noiseand/or Poisson random measures give solutions to cor-responding martingale problems. The converse, thatis, a solution of the corresponding martingale problemis a weak solution of the stochastic differential equa-tion, is well-know in the case of finite dimensional dif-fusions and has been verified in a variety of other set-tings. A general approach based on a Markov mappingtheorem will be presented that covers most, if not all,of the settings known to the author.

Regularity of the diffusion semigroupwith Dirichlet boundary conditionShigeo KUSUOKA (The University of Tokyo)

Let X(t, x) be the solution to the following SDE

dX(t, x) =d∑

k=0

Vi(X(t, x)) dBi(t)

X(0, x) = x ∈ RN .

Here we assume that Vk ∈ C∞b (RN ; RN), and thatv1

1(x) = 0, vi1(x) = 0, i = 2, . . . ,N, and v1

k(x) = 0,k = 2, . . . , d.

Let us define a family of diffusion operators Pt,t > 0 by

Pt f (x) = E[ f (X(t, x)), mins∈[0,t]

X1(s, x) > 0].

We show a certain regularity result for this operatorunder (UFG) condition.

Duality on gradient estimates andWasserstein controlsKazumasa KUWADA (Graduate School of Hu-manities and Sciences, Ochanomizu University)

On a complete Riemannian manifold, presence of alower Ricci curvature bound is known to be equivalent

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to a gradient estimate for the heat semigroup or a con-trol of the Wasserstein distance under the heat flow.In this talk, I will state a duality result between a con-trol of Wasserstein distances and a gradient estimate inmore general framework. As an application, a Wasser-stein control of a hypoelliptic diffusion on a Lie groupwill be derived.

Spectral theory for subordinate Brown-ian motions in half-lineMateusz KWASNICKI (Institute of Mathematicsand Computer Science, Wrocław University of Tech-nology)

Let ψ be a complete Bernstein function, and letη be the subordinator (i.e. nonincreasing Levy pro-cess) with characteristic exponent η. Let B be theone-dimensional Brownian motion independent fromη. Then Xt = B(ηt) is the subordinate Brownian mo-tion, and the Levy-Khinchin exponent of X is equalto ψ(ξ2). Such processes X form an important classof Levy processes, examples include symmetric stableprocesses and relativistic processes.

I will present an explicit formula for the generalizedeigenfunctions of the transition operators of the pro-cess X killed after exiting the half-line. Under someadditional assumptions, these eigenfunctions yield ageneralized eigenfunction expansion of the transitionoperators.

I will also discuss various applications of the aboveresult and their relation to fluctuation theory.

Similar results for the Cauchy (i.e. symmetric 1-stable) process were earlier obtained in [1]. The gen-eral case, described above, is studied in my recentpreprint [2].[1] T. Kulczycki, M. Kwasnicki, J. Małecki, A. Stos,

Spectral Properties of the Cauchy Process onHalf-line and Interval. Proc. London Math. Soc.(2010), to appear.

[2] M. Kwasnicki, Spectral analysis of subordinateBrownian motions in half-line. Preprint, 2010.

Residuals and goodness-of-fit tests forstationary marked Gibbs point pro-cessesFrederic LAVANCIER (Universite de Nantes,Laboratoire de Mathematiques Jean Leray, France)

The inspection of residuals is a fundamental step toinvestigate the quality of adjustment of a parametricmodel to data. For spatial point processes, the conceptof residuals has been recently proposed by Baddeleyet al (2005) as an empirical counterpart of the Camp-bell equilibrium equation for marked Gibbs point pro-cesses. We focus on stationary marked Gibbs pointprocesses and deal with asymptotic properties of resid-uals for such processes. In particular, the consistencyand the asymptotic normality are obtained for a wideclass of residuals including the classical ones (rawresiduals, inverse residuals, Pearson residuals). Theassumptions are very general and we show that theyare fulfilled for most classical Gibbs models. Basedon these asymptotic results, we define goodness-of-fittests with Type-I error theoretically controlled. To thebest of our knowledge, this is the first attempt in thisdirection for general Gibbs models. One of these testsconstitutes an extension of the quadrat counting testwidely used to test the null hypothesis of a homoge-neous Poisson point process. This contribution is acollaboration with J-F. Coeurjolly (Grenoble Univer-sity, France).

Random Time with a Given Azema Su-permartingale: A Multiplicative SystemApproachLibo LI (School of Mathematics and Statistics, Uni-versity of Sydney)

Joint work with Marek, Rutkowski

We have provided in [1], an explicit constructionof a random time when the associated Azema’s super-martingale Gt := Nte−Λt was given in advance and sat-isfies the following conditions:

(i) the process Λ is continuous increasing with Λ0 =

0 and Λ∞ = ∞,(ii) the process N is a positive continuous martingalesuch that N0 = 1,(iii) the process Ne−Λ satisfies, N0e−Λ0 = 1 and 0 <Nte−Λt < 1 for t > 0.

The approach in [1] hinges on the use of a variant ofGirsanov’s theorem combined with a judicious choiceof the Radon-Nikodym density process, which is par-tially motivated by the classic example arising in fil-tering theory.

The aim of this work is to show, with the help ofthe multiplicatives systems introduced by Meyer in [2],

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that for any given positive submartingale Y such thatY∞ = 1, there exists a random time τ on some exten-sion of the usual filtered probability space such that theAzema’s supermartingale associated with τ is givenby 1 − Y . With this technique developed, we extendthe approach considered in [1] to allow for discontinu-ities and also provide constructions of multiple corre-lated random times with given marginal Azema’s su-permartingales on the same probability space.[1] Gapeev, P., Jeanblanc, M., Li, L., and

Rutkowski, M.: Constructing Random Timeswith Given Survival Processes and Applicationsto Valuation of Credit Derivatives. Forthcomingin ”Contemporary Quantitative Finance”, C.Chiarella and A. Novikov, eds., Springer-Verlag,2010.

[2] Meyer, P.A.: Representations multiplicatives desousmartingales, d’apres Azema. Seminaire deprobabilites de Strasbourg, 13 (1979), p. 240-249

A stochastic SIS epidemic with demog-raphy: initial stages and time to extinc-tionDavid LINDENSTRAND (Stockholm Univer-sity)

We study an open population stochastic epidemicmodel from the time of introduction of the dis-ease, through a possible outbreak and to extinction.The model describes an SIS (susceptible-infective-susceptible) epidemic where all individuals, includ-ing infectious ones, reproduce at a given rate. Anapproximate expression for the outbreak probabilityis derived using a coupling argument. Further, weanalyse the behaviour of the model close to quasi-stationarity, and the time to disease extinction, withthe aid of a diffusion approximation. In this situa-tion the number of susceptibles and infectives behavesas an Ornstein-Uhlenbeck process, centred around thestationary point, for an exponentially distributed timebefore going extinct.

Multiscale Diffusion Approximations forStochastic Networks in Heavy TrafficXin LIU (University of North Carolina at ChapelHill, Department of Statistics and Operations Re-search)

We study queueing networks where the arrival andservice rates, as well as the routing structure changeover time. More precisely, we consider two inde-pendent finite state continuous time Markov processesX(t) : t ≥ 0 and Y(t) : t ≥ 0 which can be inter-preted as the random environment in which the systemis operating. The process X changes state at a muchhigher rate than the typical arrival and service times inthe system, while the reverse is true for Y . The rout-ing mechanism is governed by X. The arrival and ser-vice rates depend on the state (i.e. queue length) andthe two background Markov processes X and Y . It isshown that, under appropriate heavy traffic conditions,a properly normalized sequence of queue length pro-cesses converges weakly to a reflected Markov modu-lated diffusion process.

In order to formulate precise heavy traffic condi-tions we consider a sequence of queueing networksindexed by n ≥ 1. In the nth network, which con-sists of K service stations, the routing mechanism ismodulated by the Markov process Xn whose state x,at any given instant, determines a K × K substochas-tic matrix Px. The conditional probability that a jobcompleted at time instant t at the ith station is routedto the ith station, given Xn(t) = x, equals the (i, j)th

entry of the matrix Px. Xn has a unique stationary dis-tribution with transition times of the order O(n−(1+r0)),where r0 ∈ (1/2, 1). Additionally, we’re given a finitestate continuous time Markov process Yn with transi-tion times of the orderO(1) and infinitesimal generatorQn → Q. The arrival and service rates, which are ofthe order O(n), depend on the state and both Xn andYn. Let Qn denote the K-dimensional queue lengthprocess. We consider the Markov process (Qn,Yn),where Qn is the properly normalized queue length pro-cess. One finds that, as n → ∞, the effect of Xn is av-eraged out with respect to the stationary distribution.We show that (Qn,Yn) ⇒ (Z, Y), where Y is a finitestate continuous time Markov process with infinitesi-mal generator Q, and Z is a reflected diffusion processwith coefficients depending on (Z,Y).

The tracking error rate of the Delta-Gamma hedging strategyAzmi MAKHLOUF (Osaka university)

We analyze the convergence rate of the quadratictracking error, when a Delta-Gamma hedging strategyis used at N discrete times. The fractional regularity

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of the payoff function plays a crucial role in the choiceof the trading dates, in order to achieve optimal ratesof convergence.

Active Portfolio Selection: Outperform-ing a Benchmark PortfolioDaniel MICHELBRINK (The University of Not-tingham)

We study the portfolio selection problem of an in-vestor wishing to maximize his/her performance withrespect to some benchmark portfolio. In practice thisbenchmark portfolio is often a stock index. The stockprices are assumed to follow a geometric Brownianmotion.

The problem is formulated as an expected utilitymaximization problem. A solution is presented usingmartingale methods as well as PDE methods in formof a Hamilton Jacobi Bellman equation. The relation-ship between both will be examined.

This approach is often called active portfolio selec-tion, since the investor wishes to actively outperformthe benchmark process. This is in contrast to passiveportfolio management, where the money manager istrying to track a benchmark.

A BSDE Approach to the Sensitivity ofthe Utility Maximization ProblemMarkus MOCHA (Humboldt-Universitat zuBerlin)

Power utility maximization is a classical problem inmathematical finance that has been attacked by var-ious methods, backward stochastic differential equa-tions among them. After motivating their appearanceand presenting some potential drawbacks we providea unified treatment of the problem under a suitable ex-ponential moments conditions on the model. In partic-ular we rely on new existence, uniqueness and stabil-ity results for continuous semimartingale BSDEs un-der this assumption, which allow us to interpret thesensitivity problem of utility maximization as a stabil-ity question of these BSDEs. To be more precise weshow that the optimal wealth process and dual opti-mizer process are continuous with respect to the pa-rameter inputs, a result that holds for power utilitymaximization under cone constraints as well.

This talk is based on joint work with NicholasWestray, Humboldt Universitat zu Berlin and Quan-titative Products Laboratory.

On the behavior of the population den-sity of branching random walks in ran-dom environmentMakoto NAKASHIMA (Department of Math-ematics, Graduate School of Science, Kyoto Univer-sity)

We consider the branching random walk in d dimen-sional integer lattice with time-space i.i.d. offspringdistributions. Then, the normalization of total popu-lation is a non-negative martingale and it converges toa certain random variable almost surely. Moreover, thefollowing phase transition occurs. If the environmentis not too random, then the growth rate of the totalpopulation is the same as the one of its expectation(the regular growth phase). On the other hand, if theenvironment is random enough, then the one of the to-tal population is slower than the one of its expectation(the slow growth phase). We will look at the behaviorof the population density in each phase.

More precisely, when the process is in the regu-lar growth phase, the properly scaled population den-sity weakly converges to Gaussian measure. However,when the process is in the slow growth phase, the pop-ulation densities are infinitely often localised to a cer-tain point in Zd almost surely on the survival event.

A new approach to pricing EuropeanUnion Emission Allowance futuresAnna NAZAROVA (Chair for Energy Trading andFinance, University of Duisburg-Essen)

Liberalisation and deregulation of energy marketssince early 1990s have resulted in that prices are nowdetermined according to the fundamental economicrule of supply and demand. Introduction of the com-petitive energy markets has been a significant suc-cess because of possible consequent liquidity, effi-ciency and transparency. The basic products in theoil, gas, power, coal, emission rights and tempera-ture markets are spot, futures and forward contractsand options written on these. Energy-related spotprices demonstrate various behaviour characterised bymean-reversion, seasonality effects, regime-switching,

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spikes and exceptionally high volatility which are fardifferent from standard financial counterparts. Conse-quently, the modelling of the derivative prices is notstraightforward and depends on the specification andthe choice of risk-neutral probability [2].

In our research we will focus on the CO2 emissionsmarket. In 1997 many governments committed Kyotoprotocol accepting mandatory constraints on reductionof greenhouse gases emission. One of the mechanismsis Emission Trading System (ETS) by which of spotand derivative certificates are tradable assets. We con-sider a CO2 price as a stochastic process bounded byupper and lower boundaries, between which it followsa continuous Ito process. For this case we study var-ious boundary behaviour and provide a new groundfor their existence as well as make a generalisationfrom constant to curved boundaries. We also derive aclosed-form solution for linear derivatives for such un-derlying bounded stochastic process as well as developa general framework for the pricing of carbon deriva-tives. To support the worked out theoretical back-ground, we calibrate our model to the EU Allowance(EUA) futures prices [1].[1] F. E. Benth, A. Nazarova, and M. Wobben, A new

pricing approach to EUA futures, 2010, preprint.[2] F. E. Benth, A. Nazarova, and M. Wobben, The

pricing of derivative under bounded stochasticprocesses, 2010, preprint.

Compensators and Defaultable Securi-tiesRamin OKHRATI (Concordia University, Mon-treal, Canada)

The compensator of a process is guaranteed in cer-tain situations. Compensators can give a better under-standing of the evolution of a process through time.Besides theoretical concerns in this area, compen-sators can have important financial applications. Thisconcept is used in ”reduced form“ models in Finance.

We use semimartingale theory, together with theidea of local risk-minimization, to analyze and find thecompensator of the process (G(Xt, t)1τ>t)t≥0, whereτ = inft : Xt < 0, and G : R × [0,∞) → R+ ∪ 0 isa smooth function. This helps to understand default-able securities with payoffs in the form G(XT ,T )1τ>T ,where T > 0 is the maturity or expiration of the prod-uct. The process X is assumed to include jumps, for

instance a Levy process, and it models the underlyingrisky asset. The main effort is to obtain answers to twointeresting questions.

The first question is that given a function G asabove, how can we manage the risk of the defaultablesecurity G(XT ,T )1τ>T . In the presence of jumps, themodel is incomplete. Knowing this, the second ques-tion is if it is possible to design a customized payoffG(XT ,T )1τ>T specifically, to make the product com-pletely risk free.

Heuristics for recovery ProcessesGeorge Otieno ORWA (JKUAT)

Some models for the recovery process of cataractpatients after surgery are presented. The use of semi-Markov modeling approach is adapted in a multi-stageprocess involving acuity levels of patients. The Para-metric and Non-parametric methods of estimation areused for Maximum likelihood estimation of the so-journ time distribution. Some risk factors associatedwith the recovery process are identified by fitting bi-nary logistic regression model. The result shows thatBlood pressure and Sugar in the blood form the signif-icant risk factors associated with recovery.

Keywords: recovery process; semi-Markov; para-metric; non-parametric; logistic regression; risk fac-tors; multi-stage process.

Averaging principle for an order bookmodelMichael Christoph PAULSEN (Humboldt Uni-versity, QPL Berlin)

One approach to analyzing stochastic fluctuationsin market prices is to model the complex dynamicsof order arrivals on the microscopic level, with theaim of extracting consequences in the aggregate onthe macroscopic level. In this work we prove an av-eraging principle for key quantities (best bid/ask priceand standing buy/sell volume densities) of a randomstate-dependent order book model by taking scalinglimits when the tick size approaches zero. The averag-ing principle states that the scaled quantities convergein probability to the solution of a coupled functionalODE containing the input parameters of the model.

We prove the result in the setting of Banach spacesof martingale type 2, provide sufficient conditions on

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the model input parameters (volume, price and inter-arrival time distributions of order arrivals) for exis-tence and uniqueness of a solution for the functionalODE to hold and give two worked out examples thatrelates our work to existing models.

This is a joint work with Ulrich Horst.

Estimation of distribution function inmarked point processesZbynek PAWLAS (Department of Probability andMathematical Statistics, Faculty of Mathematics andPhysics, Charles University in Prague)

We study the asymptotic behaviour of the em-pirical process and the weighted empirical processof the marks of a stationary marked point processwhen a convex sampling window is expanding withoutbounds in all directions. We consider a random fieldmodel which corresponds to the situation when a sta-tionary random field is sampled at random locations.Our aim is to estimate nonparametrically the marginaldistribution of the random field. This model admitsdependencies between the marks but assumes that themarks and the locations are independent. The main re-sult is the weak convergence of the empirical processunder strong mixing conditions on both independentcomponents of the model. Applying an approxima-tion principle weak convergence can be also shownfor appropriately weighted empirical process definedfrom a stationary d-dimensional germ-grain processwith dependent grains. The contribution is based onthe paper [1].[1] Z. Pawlas (2009): Empirical distributions in

marked point processes, Stochastic Process. Appl.119, 4194–4209.

Lifetime Inference of Skew-Wiener Lin-ear Degradation ModelsChien-Yu PENG (Institute of Statistical ScienceAcademia Sinica)

Degradation models are widely used to assess thelifetime information of highly reliable products whichpossess quality characteristics whose degradation overtime can be related to reliability. The performance ofa degradation model depends strongly on the appro-priateness of the model describing a product’s degra-dation path. Conventionally, mixed (or random) ef-

fects formulation is one well-known approach in lit-erature. However, normality (symmetry) of randomeffects is a routine assumption in degradation models,but it may be unrealistic, obscuring important featuresof unit-to-unit variations. In this paper, motivated bylaser data, we relax this assumption by assuming thatthe random effects density is skew-normal to provideflexibility in capturing a broad range of non-normaland asymmetric behavior. Based on the extendeddegradation model, we first derive an implicit ex-pression of a product’s lifetime distribution, includingdensity, distribution functions and its correspondingmean-time-to-failure (MTT F). Furthermore, whetherthe degradation model is correctly specified or not, thevalid confidence intervals of the product’s MTT F andqth quantile can be established by using an observedinformation-based approach. Finally, the laser degra-dation data is used to illustrate the proposed model.

Annealed critical curve of a disorderedpinning model with finite range correla-tionsJulien POISAT (Universite Lyon 1)

We are interested in directed polymers pinned ata disordered and correlated interface. Significant re-sults on disordered pinning models have been ob-tained in the last few years, in particular on rele-vance/irrelevance of disorder, in the case of i.i.d. dis-order. Here, we assume that the disorder sequence is a(gaussian) q-order moving average and show that thecritical curve of the annealed model can be expressedin terms of the Perron-Frobenius eigenvalue of an ex-plicit transfer matrix. Explicit values of this annealedcritical curve for q = 1, 2, and a weak disorder asymp-totic in the general case are known. The processes aris-ing in the study of the annealed model are particularMarkov renewal processes.

Random walks in random environmentwith unbounded jumps and Knudsenbilliards with driftSerguei POPOV (University of Campinas, Brazil)

We consider a stochastic billiard in a random tubewhich stretches to infinity in the direction of the firstcoordinate vector e. This random tube is stationaryand ergodic, and also it is supposed to be in some sense

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well-behaved. The stochastic billiard can be describedas follows: when strictly inside the tube, the particlemoves straight with constant speed. Upon hitting theboundary, it is reflected randomly, according to the co-sine law: the density of the outgoing direction is pro-portional to the cosine of the angle between this direc-tion and the normal vector. In addition, we assume thethe process has a drift in the positive direction obtainedin the following way: a jump in the direction e is al-ways accepted, but if the walk attempts to jump in thenegative direction, it is accepted with probability e−λu,where u is the horizontal size of the attempted jumpand λ > 0 is a given parameter. Also, we considerone-dimensional RWREs with unbounded jumps andwithout i.i.d. assumption on the environment, whichcan be seen as a discrete analogue of the drifted ran-dom billiard in a random tube. For both processes, weprove a law of large numbers and the existence of thestationary measure for the environment seen from theparticle.

Large Liquidity Expansion of the Super-hedging costsDylan POSSAMAI (Ecole Polytechnique,Palaiseau France)

We consider a financial market with liquidity costas in Cetin, Jarrow and Protter [2] where the supplyfunction Sε(s, ν) depends on a parameter ε ≥ 0 withS0(s, ν) corresponding to the perfect liquid situation.In an earlier paper [2], the authors studied the liquid-ity premium in this model and characterized it as theunique viscosity solution of a nonlinear Black-Scholesequation, which is very similar to the one derived byBarles and Soner [1]. This nonlinear equation canonly be solved numerically as no explicit solutions areavailable. Motivated by this fact, in this paper we ob-tain rigorous asymptotic expansions for the liquiditypremium. In particular, we explicitly compute the firstterm in the expansion for a European Call option andgive bounds for the order of the expansion for a Euro-pean Digital Option, pointing out a subtle phase tran-sition for derivatives with discontinuous payoffs, sincethey induce a cost of illiquidity which vanishes at asignificantly slower rate than in the continuous payoffcase.

This is a joint work with U. Cetin, M. Soner and N.Touzi

[1] Barles, G. and Soner, H.M (1998). Option pricingwith transaction costs and a nonlinear Black-Scholes equation, Finance and Stochastics, 2,369–397.

[2] Cetin, U., Jarrow, R. and Protter, P. (2004).Liquidity risk and arbitrage pricing theory, Financeand Stochastics, 8, 311–341.

[3] Cetin, U., Soner, H.M., Touzi, N. (2007). Optionshedging for small investors under liquidity costs,preprint.

Numerical approximation of secondNeumann eigenfunctions in triangulardomainsOana RACHIERU (Transilvania University ofBrasov, Romania)

We give the numerical implementation in Mathe-matica of a numerical algorithm for the approximationof the second Neumann eigenfunction of the Lapla-ceian in a triangular domain, and we apply it to obtainsome numerical results.

Non-identifiability of the two-stateMarkovian Arrival processJosefa RAMIREZ COBO (IMUS (Institute ofMathematics, University of Seville))

In this work we consider the problem of identi-fiability of the two-state Markovian Arrival process(MAP2). In particular, we show that the MAP2 is notidentifiable and conditions are given under which twodifferent sets of parameters, induce identical stationarylaws for the observable process.

Stochastic model for second grade flu-ids: existence, uniqueness results andα-limitPaul Andre RAZAFIMANDIMBY (Depart-ment of Mathematics and Applied Mathematics, Uni-versity of Pretoria)

We investigate the stochastic equation for the mo-tion of a second grade fluid filling a bounded domainof R2. Global existence of a weak probabilistic so-lution ( and weak in the sense of partial differentialequations) is expounded. We are also able to prove the

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pathwise uniqueness of these solutions. The two re-sults yield the unique existence of a strong probabilis-tic solution. On this basis we show that under suitableconditions on the data we can construct a sequenceof solutions of the stochastic second grade fluid thatconverges to the probabilistic weak solution of thestochastic Navier-Stokes equations when the physicalparameter α tends to zero. This is a joint work withProf Mamadou Sango (Department of Mathematicsand Applied Mathematics, University of Pretoria).

On the Fatou Property for QuasiconvexFunctionsRanja REDA (Vienna University of Technology)

This paper discusses an extension of Jouini etal., showing that law-invariant functions have theFatou property under additional quasiconvexity as-sumptions. We give representation results for bothlaw-invariant cash-subadditive risk measures and law-invariant quasiconvex risk measures. Furthermore, wedevelop structure theorems for cash-subadditive, aswell as quasiconvex risk measures. Concludingly, wediscuss time-consistent law-invariant functions.

This paper is joint work with Michael Kupper andSamuel Drapeau (both Humboldt University Berlin).

Some Asymptotic Results for Near Crit-ical Branching ProcessesDominik REINHOLD (Department of Statisticsand Operations Research, University of North Car-olina at Chapel Hill)

Near critical single type Bienayme-Galton-Watson(BGW) processes are considered. It is shown that,under appropriate conditions, Yaglom distributions ofsuitably scaled BGW processes converge to that ofthe corresponding diffusion approximation. Conver-gences of stationary distributions for Q-processes andmodels with immigration to the corresponding distri-butions of the associated diffusion approximations areestablished as well. Although most of the work is con-cerned with the single type case, similar results formultitype settings can be obtained. As an illustration,convergence of Yaglom distributions of suitably scaledmultitype subcritical BGW processes to that of the as-sociated diffusion model is established.

New Estimate of the False-Positive Rateof a Bloom FilterAllen ROGINSKY (National Institute of Stan-dards and Technology (NIST))

A Bloom filter is a space-efficient data structureused for probabilistic set membership testing. Whentesting an object for set membership, a Bloom filtermay give a false positive. The analysis of the falsepositive rate is key to understanding the Bloom filterand applications that use it. We show that the clas-sic analysis for false positive rate is wrong. We derivea correct formula and show how to numerically com-pute the new, correct formula in a stable manner. Wealso prove that the new formula always results in a pre-dicted greater false positive rate than the classic for-mula. This correct formula is numerically comparedto the classic formula for relative error — for a smallBloom filter the relative error is shown to be signifi-cant.

This is a joint work with Professor Kenneth J. Chris-tensen and Dr. Miguel Jimeno, both from the Univer-sity of South Florida.

Transition Densities of Transformationsof Ito DiffusionsSanae RUJIVAN (Division of Mathematics,School of Science, Walailak University)

In this paper, we derive the forward Kolmogorovequation (FKE) associated with the formal adjointof the infinitesimal generator of transformations of agiven Ito diffusion. The fundamental solution obtainedby solving the FKE is, in fact, the transition density ofthe transformed diffusion. Moreover, we prove thatthe transition density can be represented in terms of aproduct of two functions, a Jacobian term and a com-position of the transition density of the given Ito diffu-sion and the inverse of the transformation. Finally, wepresent an application of this research in parameter es-timation in commodity markets in which the commod-ity prices are assumed to follow an extended Black-Scholes model.

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Hydrodynamic limit for exclusion pro-cesses with velocityMakiko SASADA (Graduate School of Mathe-matical Sciences, The University of Tokyo)

We consider exclusion processes with velocity onthe one-dimensional discrete lattice. It describes theevolution of a system of particles with velocity +1 or−1. Each particle moves as the totally asymmetricsimple exclusion process (TASEP) for the direction ofits velocity and the velocity of each particle changesto the opposite direction with rate γ > 0. This processcan be considered as an intermediate between simplesymmetric exclusion processes (SSEP) and TASEP inthe following sense; if γ = 0, the system evolves assame as TASEP (with the special initial condition suchthat all particles have same velocity), and if γ = ∞,formally, each particle behaves as SSEP. The model isof non-gradient and nonreversible. The number of par-ticles is a unique conserved quantity and therefore itcharacterizes the equilibrium states. We prove that theparticle density converges to the solution of a certainnonlinear diffusion equation (11) under the diffusiverescaling in space and time.

∂tρ(t, u) = ∂uDγ(ρ(t, u))∂uρ(t, u)

(11)

Diffusion coefficient, denoted by Dγ(ρ), is character-ized by a variational formula and it is strictly biggerthan that of the associated symmetric part, which inour case is 1

2 . We also obtain the asymptotic behaviorof the diffusion coefficient as γ goes to 0 or ∞. Moreprecisely, for all ρ ∈ [0, 1) and γ > 0,

12+

1 − ρ2γ≤ Dγ(ρ) ≤ 1

2+

2 − ρ4γ

holds, but also

lim supρ→1

Dγ(ρ) ≤ 12+ O(

1√γ

) as γ ↓ 0.

Especially the asymptotic behavior of the diffusion co-efficient as γ ↓ 0 at the boundary ρ = 1 differs fromthat for ρ ∈ [0, 1). I will also discuss the relation be-tween our result and the estimate of the diffusion co-efficient of TASEP.

Estimation of multivariate CARMA pro-cessesEckhard SCHLEMM (Technische UniversitatMunchen)

Multivariate Levy-driven continuous-time auto-regressive moving-average [MCARMA] processeshave been introduced recently as an extension of bothdiscrete-time vector ARMA and univariate CARMAmodels. Their use in practical situations, however, hasbeen limited so far by the lack of a theoretically soundidentification procedure. In this talk we will addressthe estimation of the parameters of a second-orderMCARMA process based on regularly spaced obser-vations using a quasi-maximum likelihood approachfor which we prove asymptotic consistency and nor-mality. We will also address the problem of obtainingpreliminary estimates to initialize the numerical maxi-mization of the quasi-likelihood. Together with canon-ical parametrizations of MCARMA processes the pro-posed estimation procedure becomes practically appli-cable. Finally, we will assess the quality of the estima-tors by the results of a simulation study.

The Symbol of an Ito Process and its Re-lations to Fine PropertiesJan Alexander SCHNURR (Technical Univer-sity Dortmund, Faculty for Mathematics, Vogelpoth-sweg 87, 44227 Dortmund)

Using a probabilistic formula we generalize the no-tion of the so called Symbol from Feller processes toIto processes (in the sense of Cinlar, Jacod, Protter andSharpe(1980)). We associate so called indices withthe symbol which are - in a certain sense - general-izations of the well known Blumenthal-Getoor indexand show that several (path-)properties of the process(e.g. p-variation, smoothness) can be characterized interms of these indices. As an example we consider thesolution of a stochastic differential equation which isdriven by a Levy process.

Random spanning trees on theSierpinski gasketMasato SHINODA (Nara Women’s University)

We define random spanning trees on the pre-Sierpinski gasket. We study some properties ofthe spanning trees and corresponding stochastic pro-cesses.

93

On integro-differential operators: Con-servativeness and Feller propertyYuichi SHIOZAWA (Graduate School of NaturalScience and Technology, Okayama University)

We give a sufficient condition for a class of integro-differential operators to possess the conservativenessand the Feller property in terms of their Levy-type ker-nels and associated measures. We then apply this con-dition to variants of operators generating stable-likeprocesses.

This talk is based on a joint work with ToshihiroUemura (Kansai University).

Exact value of the resistance exponentfor four dimensional random walk traceDaisuke SHIRAISHI (Department of Mathemat-ics, Faculty of Science, Kyoto University)

Let S be a simple random walk starting at the originin Z4. We consider G = S [0,∞) to be a random sub-graph of the integer lattice and assume that a resistanceof unit 1 is put on each edge of the graph G. Let Rn bethe effective resistance between the origin and S n. Wederive the exact value of the resistance exponent; moreprecisely, we prove that n−1E(Rn) ≈ (log n)−

12 . As an

application, we obtain sharp heat kernel estimates forrandom walk onG at the quenched level. These resultsgive the answer to the problem raised by Burdzy andLawler (1990) in four dimensions.

Stochastically perturbed gene regula-tory networksIrina SHLYKOVA (Norwegian University of LifeSciences, Department of Mathematical Sciences andTechnology)

In recent years there is an accelerating interest inthe development of stochastic models and simulationsmethods for describing the biological systems withthe intrinsic noise. In the present work we incorpo-rate stochastic effects directly to continuous and de-terministic models of non-delay and delay gene regu-latory networks. We assume that the models are en-dowed with constant white noises whose diffusion co-efficients depend on the steepness parameters of thesmooth response functions. The basic technical toolconsists in replacing the smooth response functions by

much simpler step functions. This converts a rathercomplicated system into a piecewise linear system,the dynamics of which can be described explicitly be-tween the thresholds. To fight against the singularitiesaround discontinuities we use a uniform version of thestochastic Tikhonov theorem in singular perturbationanalysis suggested by Yu. Kabanov and Yu. Perga-mentshchikov.

Fractional Fokker-Planck Equation forSubdiffusion with Space-and-Time-Dependent DriftPeter STRAKA (University of New South Wales)

Continuous Time Random Walks (CTRWs) with in-finite mean waiting times are widely used physicalmodels for subdiffusion. Scaling limits of probabil-ity densities of CTRWs are governed by fractional dif-fusion equations. This has been shown for drift co-efficients F which depend either on space [1] or ontime [2]. We [3] assume a drift coefficient F = F(x, t)which depends on both space and time and show thatthe densities pt(x) of the CTRW scaling limit are gov-erned by the fractional diffusion equation

∂

∂tpt(x) =

[∆ − ∂

∂xF(x, t)

] (∂

∂t

)1−αpt(x),

where the tails of the waiting time distributions sat-isfy a power law with parameter α ∈ (0, 1) and

(∂∂t

)1−α

denotes a Riemann-Liouville fractional derivative. Fi-nally, we discuss more general scaling limits in whichthe waiting times are taken from a triangular array.[1] Barkai, Metzler, Klafter; Phys. Rev. E 61, 2000.

[2] Sokolov, Klafter; Phys. Rev. Lett. 97, 2006.[3] Henry, Langlands, Straka; arXiv:1004.4053v1

[cond-mat.stat-mech], 2010.

Cooperation principle and disappear-ance of chaos in random complex dy-namicsHiroki SUMI (Department of Mathematics, Grad-uate School of Science, Osaka University)

We investigate the random dynamics of rationalmaps and the dynamics of semigroups of rational mapson the Riemann sphere. We show that regarding ran-dom complex dynamics of polynomials, in most cases,the chaos of the averaged system disappears, due to the

94

cooperation of the generators. We investigate the it-eration and spectral properties of transition operators.We also investigate the stability and bifurcation of ran-dom complex dynamics. We show that stable systemsare open and dense in the space of random dynam-ics of polynomials. Moreover, we show that undercertain conditions, in the limit state, “singular func-tions on the complex plane” appear. In particular, weconsider the functions T which represent the probabil-ity of tending to infinity with respect to the randomdynamics of polynomials. Under certain conditions,these functions T are complex analogues of the devil’sstaircase and Lebesgue’s singular functions. More pre-cisely, we show that these functions T are continu-ous on the Riemann sphere and vary only on the Ju-lia sets of associated semigroups. Furthermore, by us-ing ergodic theory and potential theory, we investigatethe non-differentiability and regularity of these func-tions. We find many phenomena which can hold in therandom complex dynamics and the dynamics of semi-groups of rational maps, but cannot hold in the usualiteration dynamics of a single holomorphic map. Wecarry out a systematic study of these phenomena andtheir mechanisms. For the detail, see my paper “Ran-dom complex dynamics and semigroups of holomor-phic maps” (to appear in Proc. London Math. Soc.),http://arxiv.org/abs/0812.4483.

Skew products of one-dimensional dif-fusion processes and a spherical Brow-nian motionTomoko TAKEMURA (Department of Mathe-matics, Kyoto University)

A limit theorem for the time changed skew productdiffusion processes is investigated. Skew product dif-fusion processes are given by one dimensional diffu-sion processes and the spherical Brownian motion, andthe time change is based on a positive continuous addi-tive functional with undering measure. It is shown thatthe limit process is corresponding to Dirichlet form ofnon-local type. Some examples of limit processes aregiven which lead us to Dirichlet forms with diffusionterm, jump term and killing term. We will treat re-currence and transience criteria for the skew productalso.

Large deviations on nilpotent coveringgraphsRyokichi TANAKA (Department of Mathematics,Kyoto University)

We discuss a large deviation principle of a randomwalk on a nilpotent covering graph in view of ge-ometry. As we shall observe, the behavior of a ran-dom walk at infinity is closely related to the Gromov-Hausdorff limit of an infinite graph and in the casewhere the graph admits an action of a nilpotent group,the Carnot-Caratheodory metric shows up in its limitspace.

Shadow-routing based control of flexi-ble multi-server pools in overloadTolga TEZCAN (University of Rochester)

We consider a general parallel server system modelwith multiple customer classes and several flexiblemulti-server pools, in the many-server asymptoticregime where the input rates and server pool sizes arescaled up linearly to infinity. Service of a customerbrings a constant reward, which depends on its class.The objective is to maximize the long-run reward rate.Our primary focus is on overloaded systems. Unlike inthe case when the system is non-overloaded, where themain decision is how to allocate resources to incomingcustomers, in this case it is also crucial to determinewhich customers will be admitted to the system. Wepropose a real-time, parsimonious, robust routing pol-icy, SHADOW-RM, which does not require the knowl-edge of customer input rates and does not solve anyoptimization problem explicitly, and prove its asymp-totic optimality. Then, by combining SHADOW-RMwith another policy, SHADOW-LB, proposed in ourearlier work for systems that are not overloaded, wesuggest policy SHADOW-TANDEM, which automat-ically and seamlessly detects overload and reduces toone of the schemes, SHADOW-RM or SHADOW-LB,accordingly. Extensive simulations demonstrate a re-markably good performance of proposed policies.

Risk averse asymptotics in a Black-Scholes market on a finite time horizonStefan THONHAUSER (University of Lau-sanne)

95

We consider the optimal investment and consump-tion problem in a Black-Scholes market, if the targetfunctional is given by expected discounted utility ofconsumption plus expected discounted utility of termi-nal wealth. We investigate the behavior of the optimalstrategies, if the relative risk aversion tends to infin-ity. It turns out that the limiting strategies are: do notinvest at all in the stock market and keep the rate ofconsumption constant!

Misspecification Analyses of Gammawith Inverse Gaussian ProcessesSheng Tsaing TSENG (National Tsing-Hua Uni-versity)

Degradation models are widely used these days toassess the lifetime information of highly reliable prod-ucts if there exist some quality characteristics (QC)whose degradation over time can be related to the re-liability of the product. In this study, motivated by alaser data, we investigate the mis-specification effecton the prediction of product’s MTTF (mean-time-to-failure) when the degradation model is wrongly fit-ted. More specifically, we derive an expression forthe asymptotic distribution of quasi MLE (QMLE) ofthe product’s MTTF when the true model comes fromgamma degradation process, but is wrongly treated asInverse Gaussian degradation process. The penaltyfor the model mis-specification can then be addressedsequentially. The result demonstrates that the effecton the accuracy of the product’s MTTF predictionstrongly depends on the ratio of critical value to thescale parameter of the gamma degradation process.The effects on the precision of the product’s MTTFprediction are observed to be serious when the shapeand scale parameters of the gamma degradation pro-cess are large. We then carry out a simulation studyto evaluate the penalty of the model mis-specification,using which we show that the simulation results arequite close to the theoretical ones even when thesample size and termination time are not large. Forthe reverse mis-specification problem, we carry out aMonte Carlo simulation study to examine the effect ofthe corresponding model mis-specification. The ob-tained results show that the effect of this model mis-specification is negligible.

1-D quintic NLS with white noise disper-sionYoshio TSUTSUMI (Department of Mathemat-ics, Kyoto University)

We consider the Cauchy problem for the 1-D quin-tic NLS with white noise dispersion. This equation isthought of as the limit of the NLS with random dis-persion, which describes the propagation of a signalin an optical fiber with managed dispersion. We showthe almost surely global existence of solution, no mat-ter whether the NLS is defocusing or focusing, whilethere are blowup solutions in the deternimistic focus-ing case. Our proof is based on the stochastic versionof the Strichartz estimate. This is a joint work withAnne de Bouard (Ecole Polytechnique) and ArnaudDebussche (Ecole Normale Superieure de Cachan, At-tenne de Bretagne).

Duality and Hidden Symmetries in Inter-acting Particle SystemsKiamars VAFAYI (Mathematics Institute, LeidenUniversity)

In the context of Markov processes, both in dis-crete and continuous setting, we show a general re-lation between duality functions and symmetries ofthe generator. If the generator can be written in theform of a Hamiltonian of a quantum spin system, thenthe ”hidden” symmetries are easily derived. We illus-trate our approach in processes of symmetric exclu-sion type, in which the symmetry is of SU(2) type,as well as for the Kipnis-Marchioro-Presutti (KMP)model for which we unveil its SU(1,1) symmetry. TheKMP model is in turn an instantaneous thermaliza-tion limit of the energy process associated to a largefamily of models of interacting diffusions, which wecall Brownian energy process (BEP) and which allpossess the SU(1,1) symmetry. We treat in detailsthe case where the system is in contact with reser-voirs and the dual process becomes absorbing. Ref-erence: [1] Cristian Giardina, Jorge Kurchan, FrankRedig, Kiamars Vafayi, JOURNAL OF STATISTI-CAL PHYSICS 135, 1, 25-55, APR 2009

Quenched limit theoremsDalibor VOLNY (Universite de Rouen)

96

Let (Xi) be a Markov chain, f a measurable functionon the state space. We consider the CLT for the pro-cess ( f (Xi)). If the CLT takes place for the stationarymeasure, we call it annealed. If it remains true for al-most all starting points, we call it quenched. Quenchedlimit theorems have proved being important for thestudy of e.g. infinite particle systems or of randomwalks in random scenery. We will study several limittheorems proved by martingale approximation (for ex-ample the theorems by Hannan, Maxwell-Woodroofe,Wu-Woodroffe), whether they are quenched or not.Our approach to the problem will be based more onmartingales than on Markov operators. The questionwhether the 1986 Kipnis-Varadhan CLT for reversibleMarkov chains is quenched, remains open.

Estimation in Linear Regression Mea-surement Error Models for Processeswith Uncorrelated IncrementsTiee-Jian WU (Department of Statistics, NationalCheng-Kung University)

This paper presents a method of estimating theregression and variance parameters in the linear re-gression measurement error model for a continuous-time stochastic process with uncorrelated increments,while the model considered includes the functional-,structural-, ultrastructural- and Berkson-model. Thesmall and large sample properties of the proposed es-timates are investigated.

Ergodicity of infinite dimensionalstochastic differential equations withjump noisesBin XIE (Shinshu University)

I am intending to study the ergodicity of the Markovprocess X(t) determined by the following infinite di-mensional stochastic differential equation driven by aLevy type noise:

dX(t) =(AX(t) + F(X(t))

)dt + B(X(t))dW(t)

+

∫H

G(X(t), u)q(dt, du),

where q(dt, du) denotes a compensated Poisson ran-dom measure on R+ × H.

To investigate such problem, according to the cel-ebrated Doob’s theorem, we will show the ergodic-ity of the Markov process X(t) by studying the strong

Feller property and irreducibility of the correspond-ing Markov semigroup Pt respectively. To show thestrong Feller property, we investigated the Bismut-Elworthy-Li type formula under some non-degenerateconditions. We will also give a review on the Bismut-Elworthy-Li type formula corresponding to finite orinfinite dimensional stochastic differential equationsdriven by jump noises.

On scale functions of spectrally neg-ative Levy processes with phase-typejumpsKazutoshi YAMAZAKI (Osaka University)

We study the scale function for the class of spec-trally negative Levy processes with phase-type jumps.We consider both the compound Poisson case and theunbounded variation case with diffusion components,and obtain the corresponding scale functions explic-itly. Motivated by the fact that the class of phase-typedistributions is dense in the class of all positive-valueddistributions, we propose a new approach to approxi-mating the scale function for a general spectrally neg-ative Levy process. We illustrate, in numerical exam-ples, its effectiveness by obtaining the scale functionsfor Levy processes with long-tail distributed jumps.

Realization of a finite-state mixingMarkov chain as a random walk subjectto a synchronized road coloringKenji YASUTOMI (Ritsumeikan University)

A finite-state stationary Markov chain which is ir-reducible and aperiodic is proved to be realized a ran-dom walk in directed graph subject to a synchronizingroad coloring.

This talk is based on joint work with Kouji Yano.Preprint is available at

http://arxiv.org/abs/1006.0534

Wavelet Estimation of Time-Varying Lin-ear System Parameters Based on Time-Varying Moving Average ProcessParisa YOOSEFI ZOUJ (Islamic Azad Univer-sity, Fars Science & Research Branch, Young Re-searchers club, Iran)

97

Recently there has been increased interest in time-varying linear systems. It turns out that the study oflinear systems is useful for examining the relationshipbetween different time series, the properties of linearfiltering procedures, etc. Beside, wavelet analysis andits widespread use have a great interest in differentbranches of science. So in this article, we consider thetime-varying linear system with a time-varying mov-ing average process input and find wavelet estimationof the model coefficients. Also, the model coefficientsare estimated based on kernel method and these twomethods are compared in a simulated example.

Keywords: Wavelet Estimator; Time-Varying Lin-ear System; Time-Varying Moving Average Process;Kernel Estimator.

Analytical solution for expected loss ofa collateralized loan under a quadraticGaussian default intensity processToshinao YOSHIBA (Institute for Monetary andEconomic Studies, Bank of Japan)

In this talk, we derive an analytical solution for theexpected loss of a collateralized loan, focusing on thenegative correlation between default intensity and col-lateral value. To keep non-negativity of intensity, weassume a quadratic Gaussian process for the default in-tensity. Negative correlation between default intensityand collateral value is expressed by a two-dimensionalGaussian state vector with correlated Brownian mo-tions. Given these settings, we show the expected re-covery value in the expected loss is given by a Stieltjesintegral with a measure-changed survival probability.

Asymptotic expansion for a martingalewith a mixed normal limit distributionNakahiro YOSHIDA (University of Tokyo andJST)

The quasi-likelihood estimator and the Bayesiantype estimator of the volatility parameter are in gen-eral asymptotically mixed normal. In case the limitis normal, the asymptotic expansion was derived inYoshida (PTRF 1997) as an application of the martin-gale expansion. The expansion for the asymptoticallymixed normal distribution is then indispensable to de-velop the higher-order approximation and inferencefor the volatility. The classical approaches in limit

theorems to a process with independent increments ormixture distributions do not work. We discuss asymp-totic expansion of a martingale with asymptoticallymixed normal distribution. The expansion formula isexpressed by the infinite-dimensional calculus.

Measure solutions of BSDEs and aFeynman-Kac formulaJianing ZHANG (Humboldt-Universitat zu Berlin)

A highlight of the theory on backward stochas-tic differential equations (BSDEs) is the nonlinearFeynman-Kac formula for parabolic and elliptic PDEs.The objective of this talk is to provide a measure mo-tivated access to the Feynman-Kac formula by meansof what we call measure solutions of BSDEs. Mea-sure solution is an alternative notion of BSDEs whichadopts features and ideas from the paradigm of risk-neutral pricing. We present key ideas and results onmeasure solutions and illustrate how classical BSDEsolutions are interpreted in terms of measure solutions.Based on this, we recover the Feynman-Kac formulaand, if time permits, discuss an interesting link be-tween measure solutions and the theory on the en-largement of filtrations. This talk is based on jointwork with Peter Imkeller (Humboldt-Universitat zuBerlin).

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Poster SessionsExplicit Expression of Average RunLength for Exponential CUSUMYupaporn AREEPONG (King Mongkut’s Uni-versity of Technology, North Bangkok)

The control charts CUSUM (Cumulative SUM) iswidely used in a great variety of practical applicationssuch as finance and economics, medicine, engineering,psychology, signal processing, and geology, to men-tion only several. The Average Run Length (ARL)is the most common characteristic used to designCUSUM as well as other control charts (e.g. EWMA,Shiryayev-Roberts). The ARL is usually computedvia Markov chain, Monte Carlo simulations or inte-gral equations approaches. In not many cases the so-lution for the ARL integral equation can be found inclosed form. we use the integral equation method toderive analytical solutions for the ARL integral equa-tion, when CUSUM is used. We derive the ARL forCUSUM chart assuming that the random observationsare exponentially distributed. Checking the accuracyof results, we found an excellent agreement betweennumerical solutions and the closed form expressions.

Trade-offs in pre-scheduled queueingprocesses. Application to air trans-portation.Claus Peter GWIGGNER (Electronic Naviga-tion Research Institute)

We discuss properties of a highly congested queue-ing system. The target of the analysis are understand-able strategies against congestion rather than optimalalgorithms, whose solutions are often difficult to in-terpret. Our analysis is based on an example of thedescription of air traffic flow.

Technically, we study a single server with determin-istic service times and randomly disturbed, regular ar-rivals. As shown by [1], the arrival process of sucha system is similar to a Poisson process, but the con-gestion patterns are very different. Additionally, oursystem contains a buffer, with different waiting costsinside or outside the buffer.

Our focus is the dependency of the system efficiencyon the arrival disturbances and on the buffer sizes. Forthis, we approximate the propagation of queueing de-

lays in high traffic densities and identify the conditionsfor the existence of optimal buffer sizes. In the appli-cation, these translate into a trade-off between wait-ing on low altitudes (fuel inefficient) and high altitudes(fuel efficient), even when the objective is to minimizefuel consumption [2].

Future work includes an analysis of the queueingprocess with multi-class arrivals, as well as the studyof formal proof techniques in the context of randomwalks on graphs.[1] G. Guadagni, S. Ndreca, B.Scoppola. Queueing

systems with pre-scheduled random arrivals.Technical Report. Department of Mathematics,University of Virginia, 2009.

[2] C. Gwiggner, S. Nagaoka. Efficient DelayDistribution in Air Transportation Networks.To be presented at: 24th European Conference onOperational Research. Lisbon, Portugal, 2010.

Scattering length for dual Markov pro-cessesPing HE (Department of Applied Mathematics,Shanghai University of Finance and Economics)

This talk gives an outline that generalizes Takeda’swork on scattering length for symmetric Markov pro-cesses to general case.

The integration parts by formula ofBessel random point fieldRyuichi HONDA (Graduate School of Mathemat-ics, Kyushu University)

The Bessel random point field µ is a random pointfield on [0,∞) whose n-point correlation function ρn

is given by

ρn(x1, . . . , xn) = det[K(xi, x j)]i, j=1,...,n

with determinantal kernel K defined by

K(x, y) =Jα(√

x)√

yJ′α(√

y) − Jα(√

y)√

xJ′α(√

x)2(x − y)

Here Jα is the Bessel function. It is well known thatthis random point field appears in the scaling limit ofthe eigenvalues of the Gaussian random matrices at thehard edge.

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We prove an integration by parts formula of theBessel random point field µ. More precisely, we cal-culate the log derivative of the Campbell measure νof the Bessel random point field µ. Here ν is givenby dν = ρ1(x)µxdx, where µx is the Palm measureof µ conditioned at x. As an application, we solvean infinite-dimensional stochastic differential equationthat describes the motion of the natural stochastic dy-namics reversible with respect to the Bessel randompoint field µ.

Market Information and Random FieldsLane HUGHSTON (Department of Mathematics,Imperial College London)

A simple model is proposed for situations where thepricing of an asset depends on the degree of access anagent has to the market as a whole. We fix a proba-bility space and consider an asset that delivers a sin-gle cash flow HT at time T , where time 0 denotes thepresent. The cash flow is given by a function of a ran-dom variable X. The measure on the probability spaceis taken to be the risk neutral measure, and for simplic-ity we assume that interest rates are deterministic. Themarket is represented by an n + 1-dimensional man-ifold M, one dimension of which can be understoodas the usual time variable. The remaining freedom inM is taken to represent the “extension” of the marketin a general sense (across space, across various otheragents, across various sources of information, and soforth) at a given time. We assume that M is endowedwith a volume element. For example if M is givenby Euclidean space of dimension n + 1 then the vol-ume VΣ of a measureable set Σ in M is given by theusual Lebesgue measure. We model the “information”available to a given market participant by a real-valuedset-indexed process of the form κXVΣ + βΣ. Here κ isa parameter, and βΣ is an independent bridge processthat takes the value 0 on any set that extends from time0 to time T . Thus, as T is approached, the market “re-veals” the value of X and hence the value of the cashflow. But access to a larger sector of the market at ear-lier times also “improves” the investor’s knowledge ofX, albeit with uncertainty. In the case of a Gaussianbridge process we are able to deduce an explicit for-mula for the (random) value of the asset as a func-tion of the indexing set—in other words as a functionof time and the degree of market access. Situationsinvolving multiple assets with multiple cash flows de-

pending on multiple X-factors can be treated similarly.Authors: Lane P. Hughston and Benoit Pham-Dang,Department of Mathematics, Imperial College, Lon-don SW7 2AZ, United Kingdom.

Continuous-time random and quantumwalks on the threshold network modelYusuke IDE (Department of Information SystemsCreation, Faculty of Engineering, Kanagawa Univer-sity)

Continuous-time quantum walks, which are thequantum counterparts of the random walks, have beenwidely studied on various deterministic graphs. Onthe other hand, it is well known that many real worldnetworks (graphs) are characterized by small diame-ters, high clustering, and power-law (scale-free) de-gree distributions. Various models have been proposedand they are often described by probabilistic methods.There are simulation based study of continuous-timequantum walks on probabilistic graphs, such as small-world networks (Muelken et al. 2007) and Erdos-Renyi random graph (Xu and Liu 2008). In this talk,we consider the continuous-time quantum walks onthe threshold network model which is a reasonablecandidate model having scale-free property (Masudaet al. 2004). We have quite different limit behaviorsbetween the quantum walk and the random walk onthe model starting from a vertex which is connectedwith all other vertices when the number of verticestends to infinity. For example, the quantum walker ex-hibits strong localization at the starting point, althoughthe random walker tends to spread uniformly. We dis-cuss differences between the two types of walks on themodel.

Stochastic Control: with Applications toPortfolio Optimizationludovic Tangpi NDOUNKEU (African Institutefor Mathematical, Sciences)

The main concern of this work is to describethe most relevant ideas underpinning the theory ofstochastic control. The problem of pricing in incom-plete markets, like the recent notion of indifferencepricing, along with any dynamic portfolio optimiza-tion problems can be formulated using stochastic con-trol theory. In this regard, the theory of stochas-

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tic control is of huge importance in mathematical fi-nance. We make a careful study of the theoreticalproblem in the cases of Ito-diffusions and classicalutility functions. We give the principal properties ofIto-diffusions, and then we establish the Bellman prin-ciple of dynamic optimality, from which we derive theHamilton-Jacobi-Bellman PDE. Because of the diffi-culty in solving the Hamilton-Jacobi-Bellman PDE,which is a second order fully non-linear PDE, and theassumption of smoothness made on the value func-tion to derive it, we introduce the concept of viscos-ity solutions. We apply the results to some cases ofunconstrained portfolio with different utility functions(log, exponential and power) and to a case of con-strained portfolio. We derive closed formulas for thevalue function and the optimal policy. Finally, we givesome approximations of the optimal wealth by numer-ical resolution of the stochastic differential equationthat defines it.

Keywords: Optimal control, diffusion, HJB equa-tion, portfolio optimization, viscosity solutions.

College Mathematical Readiness of theSenior High School Students in the Pub-lic Schools of District 1, Davao Citymelanie joyno ORIG (Faculty Member, Collegeof Arts and Sciences University of Mindanao, Philip-pines)

The purpose of this study is to determine the levelof mathematical proficiency of the senior high schoolsstudents enrolled in the public schools of District Iin Davao City. It also sought to determine the levelof readiness of the students for college mathematics.The students were given the mathematics achievementtest where the contents include Number Sense, Geom-etry, Probability and Statistics, Algebra and Functions.The findings of the study were used to come up with abridging program sponsored by the University of Min-danao as part of its community extension to help theincoming freshmen college students prepare for col-lege mathematics.

One–dimensional space–discrete trans-port subject to Levy perturbationsIlya PAVLYUKEVICH (Friedrich Schiller Uni-versity of Jena)

In this paper we study a one–dimensional space–discrete transport equation subject to additive Levyforcing. The explicit form of the solutions allows theiranalytic study. In particular we discuss the invarianceof the covariance structure of the stationary distribu-tion for Levy perturbations with finite second moment.The situation of more general Levy perturbations lack-ing the second moment is considered as well. Wemoreover show that some of the properties of the so-lutions are pertinent to a discrete system and are notreproduced by its continuous analogue.

On the Markov transition kernel for first-passage percolation on the ladderEckhard SCHLEMM (Technische UniversitatMunchen)

We consider the first-passage percolation problemon the ladder, that is the graph with vertex setN×0, 1and edges joining vertices at Euclidean distance equalto unity. The edge weights are assumed to be inde-pendent exponential random variables with mean one.We provide a central limit theorem for the first-passagetimes ln between the vertices (0, 0) and (n, 0), whichare defined as the length of the shortest path joining(0, 0) and (n, 0) where the length of a path is the sumof the weights of its comprising edges; we thus ex-tend earlier results about the almost sure convergenceof ln/n as n → ∞. The main part of the paper dealswith the explicit characterization of the n-step transi-tion kernels of a closely related Markov chain whichcan be used to compute explicitly the asymptotic vari-ance in the central limit theorem and is also the ba-sis for the quantitative analysis of any other statistic offirst-passage percolation times in this model. We makeextensive use of generating function techniques to ob-tain the transition kernels directly from the Chapman-Kolmogorov equations.

Spectral measure of quantum walksEtsuo SEGAWA (Tokyo Institute of Technology)

Quantum walks have interesting properties, that is,localization, an inverted-bell-shaped distribution andvariance which is square of the random walk’s one [1].Recently, Cantero et al. (2010) [2] gives the relationbetween the quantum walk and the CMV matrix. We

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discuss on how the spectral measure of the CMV ma-trix describes the properties of QW.[1] Konno, N.: Lecture Notes in Mathematics 1954

(2008) 309-452, Springer.[2] Cantero, M.J., Grunbaum, F.A., Moral, L., and

Velazquez, L.: Communications on Pure andApplied Mathematics 63 (2010) 464-507.

Probabilistic Interpretation of the For-ward Problem of Electrical ImpedanceTomographyMartin SIMON (Johannes Gutenberg UniversitatMainz)

Motivated by the development of efficient MonteCarlo methods for boundary value problems in molec-ular dynamics, such as Bossy, Champagnat, Maire andTalay [2], we establish a probabilistic interpretationfor the forward problem of electrical impedance to-mography (EIT). More precisely we use regulariza-tion, the results by Rozkosz and Słominski [4] and thetheory of Dirichlet forms to extend the Feynman-Kacformula for Neumann boundary value problems fromBencherif-Mandani and Pardoux [1] to the case of a di-vergence form operator with discontinuous coefficientand boundary data given by step functions. We thusjustify various Monte Carlo methods for the simula-tion of electrostatic measurements at the boundary ofa d-dimensional object (d = 2, 3) using a realistic elec-trode model. The setup we consider is intended to rep-resent realistic scenarios, say, heterogeneous groundwhich is modeled by a conductivity that is both dis-continuous and only partially known.[1] A. Bencherif-Madani, E. Pardoux. A Probabilistic

Formula for a Poisson Equation with NeumannBoundary Condition. Stochastic Analysis andApplications, 27:739-746, 2009.

[2] M. Bossy, N. Champagnat, S. Maire, D. Talay.Probabilistic interpretation and random walk onspheres algorithms for the Poisson-Boltzmannequation in Molecular Dynamics. To appear inMathematical Modelling and Numerical Analysis,2010.

[3] A. Lejay, S. Maire. Simulating diffusions withpiecewise constant coefficients using a kineticapproximation. Computer Methods in AppliedMechanics and Engineering, 199:2014–2023,2010.

[4] A. Rozkosz, L. Słominski. Stochasticrepresentation of reflecting diffusionscorresponding to divergence form operators.Studia Math., 139:141–174, 2000.

Uniform infinite Lorentzian triangulationand critical branching processValentin SISKO (Universidade Federal Flumi-nense)

We prove the existence of the uniform measure oninfinite causal triangulations with topology of a cylin-der through bijections with certain Galton-Watsonbranching processes conditioned on survival at infin-ity. We use this correspondence to prove convergencein distribution for the area and length of the bound-ary of a ball of radius R. In addition, we investigate theconvergence of the profike of the triangulation con-ditioned on the number of triangles. This is joint workwith A. Yambartsev, A. Zamyatin and S. Zohren.

Martingale Approach on the ExpectedFirst Passage Time of Uniformly EWMAProcedureSaowanit SUKPARUNGSEE (King Mongkut’sUniversity of Technology, North Bangkok)

The objective is to derive analytical approximationfor monitoring of changes in parameter of uniformdistribution via martingale approach. The Exponen-tially Weighted Moving Average (EWMA) procedureis used to detect to approximate the expected firstpassage times in Uniformly EWMA procedure. Theclosed form expression of a mean of false alarm timeand a mean of average delay time are presented. Theproposed expressions are compared with the resultsobtained from Monte Carlo simulation.

Scaling relations for percolation in thehigh temperature Ising Model on thesquare latticeMasato TAKEI (Department of EngineeringScience, Faculty of Engineering, Osaka Electro-Communication University)

We consider the percolation problem for the hightemperature Ising model on the two-dimensionalsquare lattice. We derive some scaling relations, pro-vided the critical exponents exist; for 2D Bernoulli

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percolation, these relations are proved by Kesten. Thisis joint work with Yasunari Higuchi (Kobe University)and Yu Zhang (University of Colorado).

Distribution of Return Point Mem-ory Configurations for Systems withStochastic InputsGrigory TEMNOV (University College Cork)

Rate-independent memory and return point mem-ory are important idealizations used to describe hys-teretic relationship between physical quantities. Thesetwo properties effectively mean that at any momentthe system memory consists of the shock values, alsocalled main extrema, of the input experienced in thepast. Such a memory, characteristic of many real-world systems, can often be efficiently modelled bythe celebrated Preisach model and its generalisations.

Some of the well-known results of Preisach mem-ory structure complement the original phenomeno-logical approach of the domain theory which con-structs the model as a superposition of non-ideal re-lays (switches), and introduces a state of the model interms of the binary states of these relays to describethe memory configuration. In applications, this stateis often a model of the physical state of the system

In our work, we assume that the initial state is nei-ther controllable nor measurable. However, we sup-pose that the initial memory configuration is the re-sult of a random input. We ask the question: what isthe distribution of the initial memory configuration?Because Preisach nonlinearity is characterized by thereturn moment memory property, an equivalent ques-tion to ask is what the distribution of the main ex-trema of the random process which creates the initialstate is. We answer this question for Brownian mo-tion, which we use as a model of the stochastic input,assuming that it was acting on the system for a longperiod of time before the moment associated with theinitial state. We also outline how the distribution of themain extrema of the Preisach memory can be obtainedfor other important types of diffusion processes.

Using Approximation Bayesian Compu-tation for testing founder effect specia-tion modelsPi-Wen TSAI (National Taiwan Normal Univer-sity)

A stochastic process known as the ”coalescent”presents a coherent statistical framework for analysisof genetic polymorphisms in population genetic. Moststatistic methods developed are based on the conceptof likelihood. Ideally, paramete inference for mod-els of interest often use either maximum likelihoodor Bayesian approaches which explicitly calculate thelikelihood of the data given the parameters. How-ever, the use of these methods is limited by the dif-ficulty of computing the likelihood function. In re-cent years, ”Approximate Bayesian Computation”, orABC, methods that approximate the likelihood basedon simulations and summary statistics have becomeincresaingly popular.

In this study, we use approximate Bayesian compu-tation to investigation four alternative speciation mod-els for the divergence between the royal spoonbill (P.regia) and its sister species the black-faced spoonbill(P. minor). The four demographic models of interestare founder effect speciation (the null model), vicari-ance speciation, non-allopatric speciation with bottle-neck and non- allopatric speciation, which are dif-fered with respec to whether the divergence processinvolved reciprocal post-divergence gene flow and/ora speciational bottleneck in P. regia. Our study showsthat speciation models that involve a protracted periodof post-divergence gene flow are much more probableexplanations than is founder effect speciation.

Asymptotics of IDS for a randomly per-turbed latticeNaomasa UEKI (Graduate School of Human andEnvironmental Studies, Kyoto University)

We consider a random Schroedinger operator wherescalar potentials are located at each site of randomlyperturbed site from an ordered lattice. This modeldescribes an intermediate situation between the com-pletely ordered lattice and the Poisson model. Forthis model we investigate the asymptotic behavior ofthe integrated density of states at the infimum of thespectrum. This problem was firstly solved by R.Fukushima. We extend the result to various situations.

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Basic properties of a long range per-turbation of the one dimensional KacmodelMaria Eulalia VARES (Centro Brasileiro dePesquisas Fisicas)

I will report on some recent research in collabora-tion with M. Cassandro (Univ. “La Sapienza”, Roma)and I. Merola (U. de L’Aquila), where we study prop-erties of a one dimensional Ising spin system with fer-romagnetic interactions given by a long range pertur-bation of the usual Kac model. We exploit a perturba-tive method similar to that used In [2,7] for short rangeinteractions in higher dimensions. The long range in-teractions decay as 1/r2 at infinity ([1.4.5.6]. The pre-sentation will be strongly based on the preprint [3].

References:[1] M. Aizenman, J. T. Chayes, L. Chayes and C. M.

Newman. Discontinuity of the magnetization in one-dimensional 1/|x − y|2 Ising and Potts models. Journ.Stat. Phys. 50, 1-40 (1988). [2] M. Cassandro, E.Presutti. Phase transitions in Ising spins with long butfinite range interactions. Markov Proc. Rel. Fields,2, 241-262 (1996) [3] M. Cassandro, I. Merola. M.E. Vares. Phase transition for a long range perturba-tion of a one-dimensional Kac model. (preprint) [4]J. Frohlich and T. Spencer. The phase transition inthe one-dimensional Ising model with 1/r2 interactionenergy. Commun. Math. Phys. 84, 87-101 (1982).[5] J. Z. Imbrie and C. M. Newman. An intermedi-ate phase with slow decay of correlations in one di-mension 1/|x−y|2 percolation, Ising and Potts models.Commum. Math. Phys. 118, 303-336 (1988). [6] D.H. U. Marchetti, V. Sidoravicius and M. E. Vares. Ori-ented percolation in one- dimensional 1/|x−y|2 perco-lation models. Journ. Stat. Phys, 139, 941-958 (2010).[7] E. Presutti. Scaling Limits in Statistical Mechanicsand Microstructures in Continuum Mechanics, Theo-retical and Mathematical Physics, Springer 2009.

Percolation for Two-Dimensional Non-Ideal GasAnatoly YAMBARTSEV (Institute of Mathe-matics and Statistics, Universidade de Sao Paulo)

We estimate locations of the regions of the percola-tion and of the non-percolation in the plane (λ, β): thePoisson rate-the inverse temperature, for interactingparticle systems in finite dimension Euclidean spaces.

Our results about the percolation and about the non-percolation are obtained under different assumptions.The intersection of two groups of the assumptions re-duces the results to two dimension Euclidean space,R2, and to a potential function of the interactions hav-ing a hard core. The technics for the percolation proofis based on a contour method which is applied to adiscretization of the Euclidean space. The technics forthe non-percolation proof is based on the coupling ofthe Gibbs field with a branching process.

Monitoring Targets and Variances onDependent Process StepsSu-Fen YANG (National Chengchi University, Tai-wan)

The variable sampling interval (VSI) weighted losscharts are proposed to monitor the quality targets andvariances on dependent process steps. The perfor-mance of the VSI weighted loss charts is measured bythe adjusted average time to signal (AATS) derived byMarkov chain approach. A numeriacl example illus-trates the application and performnce of the proposedVSI weighted loss charts. Numerical analyses showthat the VSI weighted loss charts have better perfor-mance than the fixed parameters weighted loss chartsand Shewharts charts.

Penalisation of a stable Levy process in-volving its one-sided supremumYuko YANO (Department of Mathematics, KyotoUniversity)

Roynette-Vallois-Yor [3] have considered the limitlaw of Wiener measure weighted by the supremumprocess. We call this limit theorem Brownian supre-mum penalisation.

We discuss here supremum penalisation problemfor (α, ρ)-stable Levy processes with index α ∈ (0, 2]and positivity parameter ρ ∈ (0, 1). We introduce σ-finite measure Psup by using Chaumont’s h-transformsfor Levy processes, and show that Psup unifies supre-mum penalisations. This is a generalization for stableLevy processes of Najnudel-Roynette-Yor [2] in theBrownian case.

This presentation is based on [5], and [4] with KoujiYano and Marc Yor.

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[1] L. Chaumont, Conditionings and pathdecompositions for Levy processes, Stoch.Process. Appl., 64, 39–54, 1996.

[2] J. Najnudel, B. Roynette and M. Yor, A globalview of Brownian penalisations, MSJ Memoirs,19, Mathematical Society of Japan, Tokyo, 2009.

[3] B. Roynette, P. Vallois and M. Yor, Limitinglaws associated with Brownian motion perturbedby its maximum, minimum and local time, II,Studia. Sci. Math. Hungar., 43, 295–360, 2006.

[4] K. Yano, Y. Yano and M. Yor, Penalisation ofa stable Levy process involving its one-sidedsupremum, to appear in Ann. Inst. H. PoincareProbab. Statist.

[5] Y. Yano, On a remarkable σ-finite measurewhich unifies supremum penalisation for a stableLevy process, preprint.

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