Limit theorems and the support of SDES with oblique reflections on nonsmooth domains

Abstract

In this paper we consider the Wong–Zakai type approximation and the support problem of stochastic differential equations with oblique reflections in nonsmooth domains satisfying conditions introduced by Dupuis and Ishii [4]. We first establish the limit theorem for reflected diffusions by proving that the sequence of solutions of approximating equations converge uniformly in Lp to the unique solution of the reflected stochastic differential equation. We also prove the approximate continuity and thus characterize the support of diffusions described by reflected SDEs.