Generalized FP eqn for linear SODEs system driven by additive pure jump processes

by Ito's fomula

integration by parts + variable change

TFPDE as FP eqn for overdamped Langevin eqn

TFPDE as FP eqn for overdamped Langevin eqn

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

stochastic

vs. deterministic

approach!

histogram from MC

vs. density from

TFPDE

multi-dim jump Levy dependence structure

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

LePage radial decomposition

Levy copula

directional TF

derivative along r

isometry of levy measure

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

Levy copula

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

MC/S joint PDF vs.

directional TFPDE

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

exact vs.

TFPDE in

moments

'weighted' partial

tempered fractional

derivative ! weight is v(z1,z2)