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

Yong Xu; Bin Pei; Guobin Guo

doi:10.1016/j.amc.2015.04.070

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

Yong Xu, Bin Pei, Guobin Guo

School of Mathematics and Statistics

Northwestern Polytechnical University Xian

Research output: Contribution to journal › Article › peer-review

35 Scopus citations

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.

Original language	English
Pages (from-to)	398-409
Number of pages	12
Journal	Applied Mathematics and Computation
Volume	263
DOIs	https://doi.org/10.1016/j.amc.2015.04.070
State	Published - 15 Jul 2015

Keywords

Existence and uniqueness
Lévy noise
Non-Lipschitz condition
Stability
Stochastic differential equations
Successive approximation

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10.1016/j.amc.2015.04.070

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title = "Existence and stability of solutions to non-Lipschitz stochastic differential equations driven by L{\'e}vy noise",

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

keywords = "Existence and uniqueness, L{\'e}vy noise, Non-Lipschitz condition, Stability, Stochastic differential equations, Successive approximation",

author = "Yong Xu and Bin Pei and Guobin Guo",

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doi = "10.1016/j.amc.2015.04.070",

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AU - Xu, Yong

AU - Pei, Bin

AU - Guo, Guobin

PY - 2015/7/15

Y1 - 2015/7/15

N2 - 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.

AB - 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.

KW - Existence and uniqueness

KW - Lévy noise

KW - Non-Lipschitz condition

KW - Stability

KW - Stochastic differential equations

KW - Successive approximation

UR - https://www.scopus.com/pages/publications/84929307374

U2 - 10.1016/j.amc.2015.04.070

DO - 10.1016/j.amc.2015.04.070

M3 - 文章

AN - SCOPUS:84929307374

SN - 0096-3003

VL - 263

SP - 398

EP - 409

JO - Applied Mathematics and Computation

JF - Applied Mathematics and Computation

ER -

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

Abstract

Keywords

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