A Feynman-Kac formula for stochastic Dirichlet problems

Abstract

A representation formula for solutions of stochastic partial differential equations with Dirichlet boundary conditions is proved. The scope of our setting is wide enough to cover the general situation when the backward characteristics that appear in the usual formulation are not even defined in the Itô sense.

References in corpus (3)

• Finite difference schemes for stochastic partial differential equations in Sobolev spaces
• On the solvability of degenerate stochastic partial differential equations in Sobolev spaces
• Localization errors in solving stochastic partial differential equations in the whole space

Cited by in corpus (1)

• Boundary regularity of stochastic PDEs