Stochastic differential equations for multi-dimensional domain with reflecting boundary

Abstract

In this paper we prove that there exists a unique solution of the Skorohod equation for a domain in Rd with a reflecting boundary condition. We remove the admissibility condition of the domain which is assumed in the work [4] of Lions and Sznitman. We first consider a deterministic case and then discuss a stochastic case. © 1987 Springer-Verlag.