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arXiv · 1405.3359

Existence and Stability of Solutions to Non-Lipschitz Stochastic Differential Equations Driven by Lévy Noise

Y Xu·B Pei
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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 Lévy 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 Lévy noise is also considered, and the stochastic stability is obtained in the sense of mean square.

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Y Xu, B Pei. 2014-05-14. Existence and Stability of Solutions to Non-Lipschitz Stochastic Differential Equations Driven by Lévy Noise. https://arxiv.org/abs/1405.3359

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