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

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  • Ma, Li
  • Li, Yujing
  • Zhu, Quanxin

Abstract

The regularity and stability of the solution to a class of stochastic delay differential equation driven by G-Lévy 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.

Suggested Citation

  • Ma, Li & Li, Yujing & Zhu, Quanxin, 2023. "Stability analysis for a class of stochastic delay nonlinear systems driven by G-Lévy Process," Statistics & Probability Letters, Elsevier, vol. 195(C).
    • Handle: RePEc:eee:stapro:v:195:y:2023:i:c:s0167715223000019
    DOI: 10.1016/j.spl.2023.109777
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    References listed on IDEAS

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    1. Ren, Yong & Hu, Lanying, 2011. "A note on the stochastic differential equations driven by G-Brownian motion," Statistics & Probability Letters, Elsevier, vol. 81(5), pages 580-585, May.
    2. Gao, Fuqing, 2009. "Pathwise properties and homeomorphic flows for stochastic differential equations driven by G-Brownian motion," Stochastic Processes and their Applications, Elsevier, vol. 119(10), pages 3356-3382, October.
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    Cited by:

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    2. Xia, Mingli & Liu, Linna & Fang, Jianyin & Qu, Boyang, 2024. "Exponentially weighted input-to-state stability of stochastic differential systems via event-triggered impulsive control," Chaos, Solitons & Fractals, Elsevier, vol. 182(C).
    3. Rathinasamy, Anandaraman & Mayavel, Pichamuthu, 2023. "The balanced split step theta approximations of stochastic neutral Hopfield neural networks with time delay and Poisson jumps," Applied Mathematics and Computation, Elsevier, vol. 455(C).
    4. Ivan G. Ivanov & Hongli Yang, 2023. "On the Iterative Methods for the Solution of Three Types of Nonlinear Matrix Equations," Mathematics, MDPI, vol. 11(21), pages 1-14, October.
    5. Zhengqi Ma & Shoucheng Yuan & Kexin Meng & Shuli Mei, 2023. "Mean-Square Stability of Uncertain Delayed Stochastic Systems Driven by G-Brownian Motion," Mathematics, MDPI, vol. 11(10), pages 1-16, May.
    6. Yuan, Haiyan & Zhu, Quanxin, 2024. "Practical stability of the analytical and numerical solutions of stochastic delay differential equations driven by G-Brownian motion via some novel techniques," Chaos, Solitons & Fractals, Elsevier, vol. 183(C).

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