Markov调制的无穷时滞脉冲随机泛函微分方程一般衰减意义下p阶矩和几乎必然稳定性（英文）  

pth Moment and Almost Sure Stability on General Decay for Impulsive Stochastic Functional Differential Equations with Infinite Delay and Markovian Switching

作　　者：余国胜[1] YU Guosheng(College of Mathematics and Computer Science,Jianghan University,Wuhan 430056,China)

机构地区：[1]江汉大学数学与计算机科学学院,湖北武汉430056

出　　处：《应用数学》2019年第1期19-31,共13页Mathematica Applicata

摘　　要：本文研究Markov调制的无穷时滞脉冲随机泛函微分方程一般衰减意义下p阶矩和几乎必然稳定性.我们运用Lyapunov函数,Razumikhin技巧和随机分析的方法,首先研究一般衰减意义下p阶矩稳定性.然后,运用Borel-Cantelli引理讨论一般衰减意义下几乎必然稳定性.推广并改进了已有文献的一些结果.最后,给出一个实例解释所得结果.In this paper, the problems on the pth moment and the almost sure stability on general decay for impulsive stochastic functional differential equations with infinite delay and Markovian switching are investigated. By using the Lyapunov function, the Razumikhin-type theorem and the stochastic analysis, some new results about the pth moment stability on general decay are first obtained. Then, by using the Borel-Cantelli lemma, the almost sure stability on general decay is also discussed. The results generalize and improve some results obtained in the existing literature. Finally, an example is given to illustrate the obtained results.

关 键 词：WIENER过程 矩和几乎必然稳定性 脉冲 随机泛函微分方程 一般衰减 无穷时滞 MARKOV调制 

分 类 号：O211.63[理学—概率论与数理统计]