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

Li Ma, Yujing Li and Quanxin Zhu

Statistics & Probability Letters, 2023, vol. 195, issue C

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.

Keywords: BDG-type inequality with respect to G-Lévy measure; Non-Lipschitz condition; Existence and uniqueness; Exponential stability; Stochastic delay differential equation (search for similar items in EconPapers)
Date: 2023
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Citations: View citations in EconPapers (6)

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DOI: 10.1016/j.spl.2023.109777

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