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

TL;DR

This paper establishes conditions ensuring the uniqueness and non-explosion of solutions for reflected stochastic differential equations with non-Lipschitz coefficients and non-smooth domains, expanding understanding of their behavior.

Contribution

It introduces new sufficient conditions for pathwise uniqueness and non-explosion in Skorohod SDEs with irregular coefficients and domains.

Findings

Conditions for pathwise uniqueness established

Criteria for non-explosion of solutions provided

Framework accommodates 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.