Viability for Itô stochastic systems with non-Lipschitzian coefficients and its application.

In this article, we study the viability for the multi-dimensional stochastic system described by Itô stochastic differential equations under the non-Lipschitzian assumption on the coefficients. We establish a necessary and sufficient condition for viability property with respect to a given nonempty closed convex set. And with this result, we explore the multi-dimensional comparison theorems about stochastic differential equations. [ABSTRACT FROM AUTHOR]