The central limit theorem for slow–fast systems with Lévy noise

Xiaoyu Yang; Yong Xu; Ruifang Wang; Zhe Jiao

doi:10.1016/j.aml.2021.107897

The central limit theorem for slow–fast systems with Lévy noise

Xiaoyu Yang, Yong Xu, Ruifang Wang, Zhe Jiao

School of Mathematics and Statistics

Northwestern Polytechnical University Xian

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

4 Scopus citations

Abstract

We consider a slow–fast stochastic differential system with Lévy noise. We will employ the perturbed test function method to study the normal deviation of the slow–fast system. Our main result states that the deviation can be approximated by a Gaussian process and the central limit theorem is obtained for the system.

Original language	English
Article number	107897
Journal	Applied Mathematics Letters
Volume	128
DOIs	https://doi.org/10.1016/j.aml.2021.107897
State	Published - Jun 2022

Keywords

Central limit theorem
Normal deviation
Slow–fast systems
Weak convergence

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10.1016/j.aml.2021.107897

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title = "The central limit theorem for slow–fast systems with L{\'e}vy noise",

abstract = "We consider a slow–fast stochastic differential system with L{\'e}vy noise. We will employ the perturbed test function method to study the normal deviation of the slow–fast system. Our main result states that the deviation can be approximated by a Gaussian process and the central limit theorem is obtained for the system.",

keywords = "Central limit theorem, Normal deviation, Slow–fast systems, Weak convergence",

author = "Xiaoyu Yang and Yong Xu and Ruifang Wang and Zhe Jiao",

note = "Publisher Copyright: {\textcopyright} 2021 Elsevier Ltd",

year = "2022",

month = jun,

doi = "10.1016/j.aml.2021.107897",

language = "英语",

volume = "128",

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T1 - The central limit theorem for slow–fast systems with Lévy noise

AU - Yang, Xiaoyu

AU - Xu, Yong

AU - Wang, Ruifang

AU - Jiao, Zhe

PY - 2022/6

Y1 - 2022/6

N2 - We consider a slow–fast stochastic differential system with Lévy noise. We will employ the perturbed test function method to study the normal deviation of the slow–fast system. Our main result states that the deviation can be approximated by a Gaussian process and the central limit theorem is obtained for the system.

AB - We consider a slow–fast stochastic differential system with Lévy noise. We will employ the perturbed test function method to study the normal deviation of the slow–fast system. Our main result states that the deviation can be approximated by a Gaussian process and the central limit theorem is obtained for the system.

KW - Central limit theorem

KW - Normal deviation

KW - Slow–fast systems

KW - Weak convergence

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U2 - 10.1016/j.aml.2021.107897

DO - 10.1016/j.aml.2021.107897

M3 - 文章

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SN - 0893-9659

VL - 128

JO - Applied Mathematics Letters

JF - Applied Mathematics Letters

M1 - 107897

ER -

The central limit theorem for slow–fast systems with Lévy noise

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Keywords

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