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

摘要

In this paper, successive approximation method is applied to investigate the existence and uniqueness of solutions to stochastic differential equations (SDEs) driven by Levy noise under non-Lipschitz condition which is a much weaker condition than Lipschitz one. The stability of solutions to non-Lipschitz SDEs driven by Levy noise is also considered, and the stochastic stability is obtained in the sense of mean square. (C) 2015 Elsevier Inc. All rights reserved.