On approximate continuity and the support of reflected stochastic differential equations

Abstract: In this paper we prove an approximate continuity result for stochastic differential equations with normal reflections in domains satisfying Saisho's conditions, which together with the Wong-Zakai approximation result completes the support theorem for such diffusions in the uniform convergence topology. Also by adapting Millet and Sanz-Sol\'{e}'s idea, we characterize in H\"{o}lder norm the support of diffusions reflected in domains satisfying the Lions-Sznitman conditions by proving limit theorems of adapted interpolations. Finally we apply the support theorem to establish a boundary-interior maximum principle for subharmonic functions.