chorin summer fractional_10202014

Uncertainty Quantification of SPDEs with Multi-dimensional Levy processes (Probabilistic & Deterministic Approaches) probabilistic approach deterministic approach MC PCM Fokker-Planck Equation density moment statistics

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$Page 1: Chorin summer fractional_10202014$

Uncertainty Quantification of SPDEs with Multi-dimensional Levy processes (Probabilistic & Deterministic Approaches)

probabilistic approach

deterministic approach

PCM

Fokker-Planck Equation

density

moment statistics

$Page 2: Chorin summer fractional_10202014$

1D example

PCM/CP vs. TFPDE (error of 2nd moments):

stochastic

vs. deterministic

approach!

histogram from MC

vs. density from

TFPDE

$Page 3: Chorin summer fractional_10202014$

LePage Representation of Levy Measure

(2D example)

deterministic vs. (density) probabilistic

deterministic vs. (moments) probabilistic

$Page 4: Chorin summer fractional_10202014$

Heat eqn w/ 2-dim jump processes (copula)

Levy copula

$Page 5: Chorin summer fractional_10202014$

deterministic vs. (density) probabilistic

deterministic vs. (moments) probabilistic

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