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

Yong Xu, Bin Pei, Guobin Guo

Abstract: 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.