Pathwise uniqueness and non-explosion property of Skorohod SDEs with a class of non-Lipschitz coefficients and non-smooth domains

Abstract

Here we study stochastic differential equations with a reflecting boundary condition. We provide sufficient conditions for pathwise uniqueness and non-explosion property of solutions in a framework admitting non-Lipschitz continuous coefficients and non-smooth domains.

24 pages, accepted for publication in Journal of Theoretical Probability