Nonlinear Feynman--Kac formulas for Stochastic Partial Differential Equations with Space-Time Noise

DOI10.1137/17M1163359zbMath1411.60101OpenAlexW2931635313MaRDI QIDQ4631723

Qi Zhang, Jian Song, Xiao-Ming Song

Publication date: 18 April 2019

Published in: SIAM Journal on Mathematical Analysis (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1137/17m1163359

zbMATH Keywords

stochastic partial differential equationsrandom dynamical systemsstationary solutionsFeynman-Kac formulasbackward doubly stochastic differential equationsramdom periodic solutions

Mathematics Subject Classification ID

Stochastic calculus of variations and the Malliavin calculus (60H07) Stochastic partial differential equations (aspects of stochastic analysis) (60H15) Generation, random and stochastic difference and differential equations (37H10)

Related Items (5)

Stochastic maximum principle for systems driven by local martingales with spatial parameters ⋮ BSDEs generated by fractional space-time noise and related SPDEs ⋮ Strong approximation for fractional wave equation forced by fractional Brownian motion with Hurst parameter \(H \in ( 0 , \frac{1}{2} )\) ⋮ Periodic measures and Wasserstein distance for analysing periodicity of time series datasets ⋮ High-accuracy time discretization of stochastic fractional diffusion equation

Cites Work

• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Nonlinear fractional stochastic PDEs and BDSDEs with Hurst parameter in (1/2,1)
• Pathwise random periodic solutions of stochastic differential equations
• Adapted solution of a backward stochastic differential equation
• Feynman-Kac formula for heat equation driven by fractional white noise
• Semilinear backward doubly stochastic differential equations and SPDEs driven by fractional Brownian motion with Hurst parameter in \((0,1/2)\)
• Stochastic heat equation with rough dependence in space
• Random periodic solutions of random dynamical systems
• Lectures on topics in stochastic differential equations
• Backward doubly stochastic differential equations and systems of quasilinear SPDEs
• Perfect cocycles through stochastic differential equations
• Stochastic viscosity solutions for nonlinear stochastic partial differential equations. I
• Stochastic viscosity solutions for nonlinear stochastic partial differential equations. II.
• A nonlinear stochastic heat equation: Hölder continuity and smoothness of the density of the solution
• Stationary solutions of SPDEs and infinite horizon BDSDEs
• The Malliavin Calculus and Related Topics
• Probabilistic interpretation for systems of quasilinear parabolic partial differential equations
• On a class of stochastic partial differential equations
• Weak solutions for SPDE's and backward doubly stochastic differential equations
• Stochastic PDEs driven by nonlinear noise and backward doubly SDEs

This page was built for publication: Nonlinear Feynman--Kac formulas for Stochastic Partial Differential Equations with Space-Time Noise