Markov调制的中立型变时滞SDE的矩指数稳定性  

Moment Exponential Stability of Neutral Stochastic Differential Equations with Time-variable Delay and Markov-switching

作　　者：李旭 LI Xu(School of Applied Mathematics,Nanjing University of Finance and Economics,Nanjing Jiangsu,210023)

机构地区：[1]南京财经大学应用数学学院

出　　处：《山西大同大学学报（自然科学版）》2019年第6期32-37,46,共7页Journal of Shanxi Datong University(Natural Science Edition)

基　　金：江苏省研究生科研与实践创新项目[KYCX17_1205]

摘　　要：研究了Markov调制的中立型变时滞随机微分方程的一些稳定性问题,深入探讨了Markov调制的中立型时滞随机微分方程模型的稳定性和渐近性质,特别是p(0<p≤2)阶矩指数稳定性和p阶矩有界性,利用Lyapunov函数的方法,建立零解阶矩指数稳定性的新的判定准则,推广了Markov调制的中立型变时滞随机微分方程模型下矩指数稳定性成立的p的取值范围,得到的结果是已有结果的有力补充。We investigate some stability problems of neutral stochastic differential equations with delay time-variable and Mar⁃kov-switching in this paper and further study on the[p]th moment exponential stability and asymptotic properties of stochastic neutral differential equations with Markov-switching and time-variable delay,especially the[p]th moment exponential stability and the[p]th moment asymptotical boundedness.By using the method of Lyapunov function,some new criterion for the[p0<p≤2]th moment exponen⁃tial stability are derived,which extend the range of[p]value.Our results are the favorable supplement to the previous results.Finally,some examples are given to illustrate the effectiveness of our results.

关 键 词：中立型随机微分方程 LYAPUNOV函数 阶矩指数稳定性 阶矩有界性 

分 类 号：O211.6[理学—概率论与数理统计]