一般衰减率下脉冲随机泛函微分方程的p阶矩稳定性  

p-Moment Stability with General Decay Rate of Impulsive Stochastic Functional Differential Equations

作　　者：张秀英[1] 苏春华 ZHANG Xiuying;SU Chunhua(Public Education Department,Zhengzhou Railway Vocational&Technical College,Zhengzhou 451460;College of Mathematics and Statistics,Xinyang Normal University,Xinyang 464000)

机构地区：[1]郑州铁路职业技术学院公共教学部,郑州451460 [2]信阳师范学院数学与统计学院,信阳464000

出　　处：《系统科学与数学》2019年第8期1184-1200,共17页Journal of Systems Science and Mathematical Sciences

基　　金：国家自然科学基金(11701496)资助课题

摘　　要：研究了具有一般衰减率的脉冲随机泛函微分方程的p阶矩稳定性问题.利用Lyapunov泛函法、随机分析理论和文章所建立的脉冲微分不等式,得到了该方程在一般衰减率下p阶矩稳定性和几乎必然稳定性的一些充分性条件.所得的这些条件既简单又具有一般性,并被应用于讨论了一般衰减率下脉冲随机时滞微分方程的p阶矩稳定性问题.实例表明,所得结果是有效的和实用的.This paper investigates the p-moment stability with general decay rate of impulsive stocliastic functional differential equations.Based on Lyapunov functional method.stochastic analysis theory and the impulsive differential inequality established in this paper,some sufficient conditions on p-moment stability and almost sure stability with general decay rate are derived.The obtained results are more general and simple,and are used to deal with impulsive stochastic delay differential equations.Finally,two numerical examples are given to demonstrate the effectiveness of the proposed results.

关 键 词：脉冲 随机泛函微分方程 脉冲微分不等式 DINI导数 一般衰减率 p阶矩稳定 

分 类 号：O1[理学—数学]