uncertainty quantification of SPDEs with multi-dimensional Levy processes

1. Generalized FP eqn for linear SODEs system driven by additive pure jump processes by Ito's fomula integration by parts + variable change

2. TFPDE as FP eqn for overdamped Langevin eqn

3. 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

4. Heat eqn w/ 2-dim jump processes (LePage) multi-dim jump Levy dependence structure LePage radial decomposition Levy copula directional TF derivative along r isometry of levy measure

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

6. Heat eqn w/ 2-dim jump processes (LePage) MC/S joint PDF vs. directional TFPDE

7. Heat eqn w/ 2-dim jump processes (copula) exact vs. TFPDE in moments 'weighted' partial tempered fractional derivative ! weight is v(z1,z2)

uncertainty quantification of SPDEs with multi-dimensional Levy processes

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uncertainty quantification of SPDEs with multi-dimensional Levy processes

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uncertainty quantification of SPDEs with multi-dimensional Levy processes