中文摘要：

利用Banach不动点方法研究了一类中立型多变时滞随机微分方程零解的均方渐近稳定性,同时对所得的零解均方渐近稳定给出了严格的证明。之前,几乎所有的专家和学者在利用Banach不动点方法研究随机微分方程的稳定性时,主要是通过引入合适的函数来完成和实现。和大多数研究的方法不同,在研究多变时滞随机微分方程稳定性时,文中将引入的函数拆分,然后利用拆分后的函数去构造算子,再利用Banach不动点研究其稳定性,推广和改进了前人研究的结果。文中最后给出了一个例题来说明结果。

英文摘要：

We consider a class of linear scalar neutral stochastic differential equation with some variable delays and give conditions to ensure that the zero solution is asymptotically stable in mean square by means of Banach fixed point meth-od.Previously,when almost all the experts and scholars study the stability of stochastic differential equations by means of Banach fixed point,it is usually achieved and accomplished by introducing appropriate functions.Being different from most other study methods,we will split the introduced functions when studying the stability of stochastic differential equations with some variable delays to construct the operator in this paper.Then,study its stability by ways of Banach fixed point,promote and improve the previous studies.Also an example was given to illustrate the results in the paper.