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.
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