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

TL;DR

This paper investigates the Wong-Zakai approximation for solutions to reflecting stochastic differential equations in Euclidean domains, establishing convergence results under broad conditions.

Contribution

It provides the first rigorous proof of $L^p$ convergence for Wong-Zakai approximations in reflecting SDEs on general domains.

Findings

Proves $L^p$ convergence of Wong-Zakai approximations

Establishes convergence in the space of continuous functions

Applies to a wide class of Euclidean domains

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 $D$.