Obstacle problem for SPDE with nonlinear Neumann boundary condition via reflected generalized backward doubly SDEs

TL;DR

This paper establishes a representation for the stochastic viscosity solution of semi-linear reflected SPDEs with nonlinear Neumann boundary conditions, using reflected generalized backward doubly stochastic differential equations.

Contribution

It introduces a novel connection between reflected generalized backward doubly stochastic differential equations and the stochastic viscosity solutions of certain SPDEs with boundary conditions.

Findings

Representation formula for solutions of reflected SPDEs.

Connection between reflected backward doubly SDEs and SPDE solutions.

Framework for analyzing nonlinear boundary conditions in SPDEs.

Abstract

This paper is intended to give a representation for stochastic viscosity solution of semi-linear reflected stochastic partial differential equations with nonlinear Neumann boundary condition. We use its connection with reflected generalized backward doubly stochastic differential equations.