一类中立型随机泛函微分方程解的p阶矩在一般衰减率下的稳定性  

The pth Moment Stability with General Decay Rate of the Solutions for a Class of Neutral Stochastic Functional Differential Equations

作　　者：梁青[1] LIANG Qing(College of Mathematics and Statistics,Hainan Normal University,Haikou 571158)

机构地区：[1]海南师范大学数学与统计学院,海口571158

出　　处：《系统科学与数学》2024年第4期1189-1206,共18页Journal of Systems Science and Mathematical Sciences

基　　金：国家自然科学基金(11861029);海南省高等学校教育教学改革研究项目(hnjg2022-40)资助课题。

摘　　要：研究了一类具有Markov切换和Lévy噪声的中立型随机泛函微分方程解的稳定性.首先,构造一个辅助的泛函微分方程,然后,在适当的假设条件下利用辅助方程的参数变化公式、不等式技巧以及比较定理,得到了该中立型随机泛函微分方程的解在一般衰减率下p阶矩稳定的两个充分条件,推广了已有文献中的结果.最后,通过举例和给出数值模拟说明了结果的有效性.In this paper,the stability of the solutions for a class of neutral stochastic functional differential equations with Markovian switching and Levy noise is investigated.First,an auxiliary functional differential equation is constructed.Then,under some suitable assumptions two sufficient conditions for the pth moment of the solutions for the neutral stochastic functional differential equations to be stable with general decay rate are obtained by means of the formula for the variation of parameters of the auxiliary functional differential equation,some inequality technique and comparison principle.The obtained results generalize the results in some earlier publications.Finally,two examples and numerical simulations are given to illustrate the effectiveness of the results.

关 键 词：随机泛函微分方程 一般衰减率 Markov切换 Lévy噪声 It?公式 

分 类 号：O211.63[理学—概率论与数理统计]