Stability analysis for a class of stochastic delay nonlinear systems driven by G-Levy Process

被引：2

作者：

Ma, Li ^{[1
]}

Li, Yujing ^{[1
]}

Zhu, Quanxin ^{[2
]}

机构：

[1] Hainan Normal Univ, Dept Math & Stat, Key Lab, Minist Educ, Haikou 571158, Peoples R China

[2] Hunan Normal Univ, Sch Math & Stat, CHP LCOCS, Changsha 410082, Peoples R China

来源：

STATISTICS & PROBABILITY LETTERS | 2023年 / 195卷

基金：

中国国家自然科学基金;

关键词：

BDG-type inequality with respect toG-Levy; measure; Non-Lipschitz condition; Existence and uniqueness; Exponential stability; Stochastic delay differential equation;

D O I：

10.1016/j.spl.2023.109777

中图分类号：

O21 [概率论与数理统计]; C8 [统计学];

学科分类号：

020208 ; 070103 ; 0714 ;

摘要：

The regularity and stability of the solution to a class of stochastic delay differential equation driven by G-Levy processes are studied in this paper. Firstly, we introduce a new Burkholder-Davis-Gundy (BDG) inequality involving the jump measure. Secondly, we use the BDG inequality to establish the existence and uniqueness of the solution under non-Lipschitz condition. Thirdly, we establish the existence, uniqueness, quasi -sure exponential stability and pth moment exponential stability of the solution under local Lipschitz condition and one-sided polynomial growth condition.(c) 2023 Elsevier B.V. All rights reserved.

引用

页数：11

共 25 条

[1]

Applebaum D., 2009, Camb. Stud. Adv. Math., VSecond

[2] On the Existence and Uniqueness of Solutions to Stochastic Differential Equations Driven by G-Brownian Motion with Integral-Lipschitz Coefficients [J].

Bai, Xue-peng ;

Lin, Yi-qing .

ACTA MATHEMATICAE APPLICATAE SINICA-ENGLISH SERIES, 2014, 30 (03) :589-610

[3]

Faizullah F., 2012, NAT FORSCH A, V67a

[4]

Faizullah F., 2019, J COMPUT ANAL APPL, V26, P8190

[5]

Faizullah F, 2020, Arxiv, DOI arXiv:2005.01930

[6] Existence and stability of solutions to non-linear neutral stochastic functional differential equations in the framework of G-Brownian motion [J].

Faizullah, Faiz ;

Bux, M. ;

Rana, M. A. ;

Rahman, Ghaus Ur .

ADVANCES IN DIFFERENCE EQUATIONS, 2017,

[7] On the pth moment estimates of solutions to stochastic functional differential equations in the G-framework [J].

Faizullah, Faiz .

SPRINGERPLUS, 2016, 5

[8] Pathwise properties and homeomorphic flows for stochastic differential equations driven by G-Brownian motion [J].

Gao, Fuqing .

STOCHASTIC PROCESSES AND THEIR APPLICATIONS, 2009, 119 (10) :3356-3382

[9]

Hu MS, 2009, Arxiv, DOI [arXiv:0911.3533, 10.3934/puqr.2021001]

[10]

Li Q., 2018, APPL ANAL, V15

← 1 2 3 →