中立型随机泛函微分方程的Khasminskii型定理

本文对中立型随机泛函微分方程建立了Khasminskii型定理,这个定理显示在局部Lipschitz条件但是不要求线性增长的条件下,中立型随机泛函微分方程存在一个全局解.本文的这个解存在性条件可以包含更广的一类非线性中立型随机泛函微分方程.最后,本文给出一个例子来阐述我们的思想.

Khasminskii-Type Theorems for Neutral Stochastic Functional Differential Equations

This paper establishes the Khasminskii-Type theorems for neutral stochastic functional differential equations, which shows that neutral stochastic functional differential equations have nonexplosion solutions with the local Lipschitz condition but neither the linear growth condition.The conditons in this paper may cover a wide class of nonlinear neutral stochastic functional differential equations.Finally, this paper examine an example to illustrate our idea.