一类具有泊松跳的脉冲中立型随机泛函微分方程的存在性及稳定性研究

数学物理学报 ›› 2023, Vol. 43 ›› Issue (4): 1221-1243.

一类具有泊松跳的脉冲中立型随机泛函微分方程的存在性及稳定性研究

何旭阳(),毛明志^*(),张腾飞

中国地质大学(武汉)数学与物理学院武汉 430070

收稿日期:2022-06-22 修回日期:2023-02-14 出版日期:2023-08-26 发布日期:2023-07-03
通讯作者: 毛明志 E-mail:1202010933@cug.edu.cn;mingzhi-mao@163.com
作者简介:何旭阳，E-mail: 1202010933@cug.edu.cn
基金资助:
中国地质大学(武汉)基础研究中心基金(CUGSX01)

Existence and Stability of a Class of Impulsive Neutral Stochastic Functional Differential Equations with Poisson Jump

He Xuyang(),Mao Mingzhi^*(),Zhang Tengfei

School of Mathematics and Physics, China University of Geosciences $($Wuhan$),$ Wuhan 430070

Received:2022-06-22 Revised:2023-02-14 Online:2023-08-26 Published:2023-07-03
Contact: Mingzhi Mao E-mail:1202010933@cug.edu.cn;mingzhi-mao@163.com
Supported by:
FRFC(CUGSX01)

摘要/Abstract

摘要：

该文考虑一类具有泊松跳的脉冲中立型随机泛函微分方程温和解的存在唯一性以及指数稳定性. 利用逐次逼近和Picard迭代方法, 证明了在Hilbert空间中温和解的存在性; 其次, 通过Banach不动点原理, 给出了均方指数稳定和几乎必然指数稳定的充分条件.

关键词: 存在唯一性, 中立型随机泛函微分方程, 温和解, 泊松跳跃, 指数稳定性

Abstract:

In this paper, we consider the existence, uniqueness and exponential stability of mild solutions for a class of impulsive neutral stochastic functional differential equations with Poisson jumps.By using successive approximation and Picard iteration method, the existence of mild solutions in Hilbert space is proved. Secondly, the sufficient conditions for the mean square exponential stability and almost certain exponential stability are given by Banach's fixed point principle.

Key words: Existence and uniqueness, Netral stochastic functional differential equations, Mild solution, Poisson jumps, Exponential stability

中图分类号:

O211.4

何旭阳,毛明志,张腾飞. 一类具有泊松跳的脉冲中立型随机泛函微分方程的存在性及稳定性研究[J]. 数学物理学报, 2023, 43(4): 1221-1243.

He Xuyang,Mao Mingzhi,Zhang Tengfei. Existence and Stability of a Class of Impulsive Neutral Stochastic Functional Differential Equations with Poisson Jump[J]. Acta mathematica scientia,Series A, 2023, 43(4): 1221-1243.

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