Stability analysis for a class of stochastic delay nonlinear systems driven by G-Lévy process (Q6101717)

The authors study regularity and stability of solutions to a class of stochastic delay differential equations driven by G-Lévy processes. The notion of such processes was introduced about 15 years ago as an extension of G-Brownian motion with a sublinear expectation. One of the first results in the article is a Burkholder-Davis-Gundy (BDG) inequality for the jump measure. Then the BDG inequality is used to show the existence and uniqueness of solutions under non-Lipschitz condition. Under local Lipschitz and one-sided polynomial growth conditions, the authors in addition establish quasi-sure exponential stability and the \(p\)th moment exponential stability of the solution.