一类Markov切换的脉冲随机偏泛函微分方程的均方稳定性分析  

Mean Square Stability Analysis for a Class of Impulsive Stochastic Partial Functional Differential Equations with Markovian Switching

作　　者：李钊 李树勇 LI Zhao;LI Shuyong(College of Computer Science,Chengdu University,Chengdu 610106;College of Mathematics Science,Sichuan Normal University,Chengdu 610066;School of Mathematics and Physics,Mianyang Teachers'College,Mianyang 621000)

机构地区：[1]成都大学计算机学院,成都610106 [2]四川师范大学数学科学学院,成都610066 [3]绵阳师范学院数理学院,绵阳621000

出　　处：《系统科学与数学》2020年第12期2225-2236,共12页Journal of Systems Science and Mathematical Sciences

基　　金：国家自然科学基金(11571245)资助课题。

摘　　要：研究了一类Markov切换的脉冲随机偏泛函微分方程的均方稳定性问题.首先,利用脉冲时滞微分不等式技巧和随机分析理论,建立了一类Markov切换的脉冲随机偏泛函微分方程的比较原理.然后,应用比较原理得到了这类方程的几个新的稳定性判据.最后,通过实例验证了所提出的结果的有效性.This paper investigates the mean square stability problem for a class of stochastic partial functional differential equations with Markovian switching.By employing impulsive delay differential inequality technique and stochastic analysis theory,comparison principle for a class of stochastic partial functional differential equations with Markovian switching is firstly established.Then,the comparison principle is applied to obtain several novel stability criteria of such equation.Finally,an example is provided to show the effectiveness of the proposed results.

关 键 词：Markov切换 脉冲 随机偏泛函微分方程 比较原理 均方稳定 

分 类 号：O211.63[理学—概率论与数理统计]