The averaging principle for stochastic differential equations with Caputo fractional derivative

Wenjing Xu; Wei Xu; Shuo Zhang

doi:10.1016/j.aml.2019.02.005

The averaging principle for stochastic differential equations with Caputo fractional derivative

Wenjing Xu
, Wei Xu
, Shuo Zhang

School of Mathematics and Statistics

Northwestern Polytechnical University Xian

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

63 Scopus citations

Abstract

This paper presents an averaging principle for Caputo fractional stochastic differential equations (FSDEs) driven by Brown motion. Under some assumptions, the solutions to FSDEs can be approximated by solutions to averaged stochastic systems in the sense of mean square. The analyses of solutions to systems before and after averaging, allow to extend the classical Khasminskii approach to Caputo fractional stochastic equations.

Original language	English
Pages (from-to)	79-84
Number of pages	6
Journal	Applied Mathematics Letters
Volume	93
DOIs	https://doi.org/10.1016/j.aml.2019.02.005
State	Published - Jul 2019

Keywords

Averaging principle
Caputo fractional derivative
Stochastic differential equations

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10.1016/j.aml.2019.02.005

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title = "The averaging principle for stochastic differential equations with Caputo fractional derivative",

abstract = "This paper presents an averaging principle for Caputo fractional stochastic differential equations (FSDEs) driven by Brown motion. Under some assumptions, the solutions to FSDEs can be approximated by solutions to averaged stochastic systems in the sense of mean square. The analyses of solutions to systems before and after averaging, allow to extend the classical Khasminskii approach to Caputo fractional stochastic equations.",

keywords = "Averaging principle, Caputo fractional derivative, Stochastic differential equations",

author = "Wenjing Xu and Wei Xu and Shuo Zhang",

note = "Publisher Copyright: {\textcopyright} 2019 Elsevier Ltd",

year = "2019",

month = jul,

doi = "10.1016/j.aml.2019.02.005",

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AU - Xu, Wei

AU - Zhang, Shuo

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N2 - This paper presents an averaging principle for Caputo fractional stochastic differential equations (FSDEs) driven by Brown motion. Under some assumptions, the solutions to FSDEs can be approximated by solutions to averaged stochastic systems in the sense of mean square. The analyses of solutions to systems before and after averaging, allow to extend the classical Khasminskii approach to Caputo fractional stochastic equations.

AB - This paper presents an averaging principle for Caputo fractional stochastic differential equations (FSDEs) driven by Brown motion. Under some assumptions, the solutions to FSDEs can be approximated by solutions to averaged stochastic systems in the sense of mean square. The analyses of solutions to systems before and after averaging, allow to extend the classical Khasminskii approach to Caputo fractional stochastic equations.

KW - Averaging principle

KW - Caputo fractional derivative

KW - Stochastic differential equations

UR - https://www.scopus.com/pages/publications/85061600604

U2 - 10.1016/j.aml.2019.02.005

DO - 10.1016/j.aml.2019.02.005

M3 - 文章

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SN - 0893-9659

VL - 93

SP - 79

EP - 84

JO - Applied Mathematics Letters

JF - Applied Mathematics Letters

ER -

The averaging principle for stochastic differential equations with Caputo fractional derivative

Abstract

Keywords

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