On approximations for reflected SDEs and SPDEs with Neumann boundary conditions

Abstract

In this paper we study an approximation for reflected stochastic differential equations in non-smooth domains by replacing the driving Brownian motion with its smooth approximation and prove that the solutions of approximating equations converge in the mean square to the solution of the Stratonovich reflected stochastic differential equation. We also study the smooth approximation for Neumann-type semilinear stochastic partial differential equations, which is completed through establishing the convergence in $ L^2 $ of backward doubly stochastic differential equations coupled with reflected SDEs.