中文摘要：

本文是我们之前工作的延伸,本文作者和殷荣城（2013）在单调型条件下考察了随机微分方程的θ方法的均方稳定性.在之前的结论中,我们考虑的是不带延迟的随机系统的均方稳定性.而本文,我们希望进一步考虑带延迟的随机系统的几乎必然稳定性.本文在修改后的Khasminskii条件下得到随机延迟微分方程θ方法的几乎必然指数稳定性.该结果使现有结论得到可观的推进.

英文摘要：

This paper is a continuation of our previous paper（2013）, in which, the author, with YIN examined the moment stability of the θmethod for SDEs with monotonetype condition. In the previous results, we consider the moment exponential stability of stochastic system without delay. In this paper we further consider stochastic system with delay, and examined almost sure stability. Under modified Khasminskii condition, this paper will give the almost sure exponential stability of the θ method for SDDEs. This improves the existing results considerably.