On Lp-strong convergence of an averaging principle for non-Lipschitz slow-fast systems with Lévy noise

Yong Xu; Hongge Yue; Jiang Lun Wu

doi:10.1016/j.aml.2020.106973

On L^p-strong convergence of an averaging principle for non-Lipschitz slow-fast systems with Lévy noise

Yong Xu, Hongge Yue, Jiang Lun Wu

School of Mathematics and Statistics

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

9 Scopus citations

Abstract

We study L^p-strong convergence for coupled stochastic differential equations (SDEs) driven by Lévy noise with non-Lipschitz coefficients. Utilizing Khasminkii's time discretization technique, the Kunita's first inequality and Bihari's inequality, we show that the slow solution processes converge strongly in L^p to the solution of the corresponding averaged equation.

Original language	English
Article number	106973
Journal	Applied Mathematics Letters
Volume	115
DOIs	https://doi.org/10.1016/j.aml.2020.106973
State	Published - May 2021

Keywords

Averaging principle
Lévy noise
Non-Lipschitz coefficients
Slow-fast systems

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10.1016/j.aml.2020.106973

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title = "On Lp-strong convergence of an averaging principle for non-Lipschitz slow-fast systems with L{\'e}vy noise",

abstract = "We study Lp-strong convergence for coupled stochastic differential equations (SDEs) driven by L{\'e}vy noise with non-Lipschitz coefficients. Utilizing Khasminkii's time discretization technique, the Kunita's first inequality and Bihari's inequality, we show that the slow solution processes converge strongly in Lp to the solution of the corresponding averaged equation.",

keywords = "Averaging principle, L{\'e}vy noise, Non-Lipschitz coefficients, Slow-fast systems",

author = "Yong Xu and Hongge Yue and Wu, {Jiang Lun}",

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AU - Yue, Hongge

AU - Wu, Jiang Lun

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Y1 - 2021/5

N2 - We study Lp-strong convergence for coupled stochastic differential equations (SDEs) driven by Lévy noise with non-Lipschitz coefficients. Utilizing Khasminkii's time discretization technique, the Kunita's first inequality and Bihari's inequality, we show that the slow solution processes converge strongly in Lp to the solution of the corresponding averaged equation.

AB - We study Lp-strong convergence for coupled stochastic differential equations (SDEs) driven by Lévy noise with non-Lipschitz coefficients. Utilizing Khasminkii's time discretization technique, the Kunita's first inequality and Bihari's inequality, we show that the slow solution processes converge strongly in Lp to the solution of the corresponding averaged equation.

KW - Averaging principle

KW - Lévy noise

KW - Non-Lipschitz coefficients

KW - Slow-fast systems

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DO - 10.1016/j.aml.2020.106973

M3 - 文章

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VL - 115

JO - Applied Mathematics Letters

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ER -

On L^p-strong convergence of an averaging principle for non-Lipschitz slow-fast systems with Lévy noise

Abstract

Keywords

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