Existence and Stability of Solutions to Non-Lipschitz Stochastic Differential Equations Driven by L\'evy Noise
Dynamical Systems
2014-05-15 v1
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.
Keywords
Cite
@article{arxiv.1405.3359,
title = {Existence and Stability of Solutions to Non-Lipschitz Stochastic Differential Equations Driven by L\'evy Noise},
author = {Y Xu and B Pei},
journal= {arXiv preprint arXiv:1405.3359},
year = {2014}
}