Abstract

In this paper, we focus on the problem of viability property for the multi-dimensional stochastic differential equations, where the coefficients of the stochastic differential equations may be random and discontinuous in the time variable. First, we establish a necessary and sufficient condition for viability property with respect to a given non-empty closed convex set. And furthermore, with the help of this result, we also study the multi-dimensional comparison theorems about stochastic differential equations.

中文翻译：

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多维随机微分方程的生存性及其在比较定理中的应用

摘要

在本文中，我们关注多维随机微分方程的生存性问题，其中随机微分方程的系数在时间变量上可能是随机的和不连续的。首先，我们针对给定的非空闭凸集建立生存能力属性的充分必要条件。此外，借助这一结果，我们还研究了随机微分方程的多维比较定理。