Existence and Stability of Solutions to Non-Lipschitz Stochastic Differential Equations Driven by L\'evy Noise

Abstract

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