连续变量型随机脉冲差分方程零解的均方指数稳定性

Exponential Stability in Mean Square of Impulsive Stochastic Difference Equations with Continuous Time

研究了连续变量型随机脉冲差分方程的均方指数稳定性,可以弥补此问题的空白.在研究过程中不仅脱离了一般的方法,例如Lyapunov方法、It^o公式等等,而且还引用了一个重要的差分不等式来获取好的结果.同样,所得结果也适用于没有脉冲的情况.

So far there are few results on the exponential stability in mean square for impulsive stochastic difference equations with continuous time. The main aim of this paper is to close this gap. Dissimilarly, we don＇t make use of the general methods such as Lyapunov methods, Ito formula and so forth. However, we obtain the desired result by establishing a difference inequality with continuous time. Moreover. the obtained result can be applied to stochastic difference equations, without impulsive effects, with continuous time. In the end, we construct an example to illustrate the effectiveness of our result