比较原理与一类具有时滞和马尔科夫切换的随机抛物方程组的稳定性分析（英文）

Comparison Principle and Stability Analysis of a Class of Stochastic Parabolic Equations with Delay and Markovian Switching

研究一类具有时滞和马尔科夫切换的随机抛物方程组的均方稳定性.通过建立比较原理,运用时滞微分不等式和随机分析技巧,获得了该系统的均方稳定、均方一致稳定、均方渐近稳定和均方指数稳定.最后,给出了主要定理的一个应用实例.

This paper investigates the mean square stability for stochastic parabolic equations with delay and Markovian switching. By establishing the comparison principle, using delay differential inequality and stochastic analysis techniques, the mean square stability, mean square uniform stability, mean square asymptotic stability and mean square exponential stability for the system are obtained. Finally, an example is given to illustrate the main theoretical result.