Approximation Theorems For Reflected Stochastic Differential Equations

TL;DR

This paper establishes a general approximation framework for reflected stochastic differential equations in bounded domains, encompassing various approximation methods like Wong-Zakai and mollifier approximations.

Contribution

It provides a unified approximation theorem for reflected SDEs in bounded domains, extending existing methods under a common framework.

Findings

Proves a general approximation theorem for reflected SDEs.

Includes Wong-Zakai and mollifier approximations as special cases.

Extends previous results to broader classes of reflected SDEs.

Abstract

In this paper we prove a general approximation result for reflected stochastic differential equations in bounded domains satisfying conditions reorganized by Ren and Wu. Then we show that it includes Wong-Zakai approximation, mollifier approximation, etc.