Wong-Zakai approximation of solutions to reflecting stochastic differential equations on domains in Euclidean spaces

Abstract

In this paper, we study the Wong-Zakai approximation of the solution to the stochastic differential equation on a domain $D$ in a Euclidean space with normal reflection at the boundary. We prove the $L^p$ convergence of the approximation in $C([0,T]\to \bar{D})$ under some general conditions on $D$.