Existence and stability of solutions to non-Lipschitz stochastic differential equations driven by Lévy noise

In this paper, successive approximation method is applied to investigate the existence and uniqueness of solutions to stochastic differential equations (SDEs) driven by Lévy noise under non-Lipschitz condition which is a much weaker condition than Lipschitz one. The stability of solutions to non-Lipschitz SDEs driven by Lévy noise is also considered, and the stochastic stability is obtained in the sense of mean square.