An averaging principle for stochastic differential equations of fractional order 0 < α

An averaging principle for stochastic differential equations of fractional order 0 < α < 1

Published:2020-06-01 Issue:3 Volume:23 Page:908-919
ISSN:1314-2224
Container-title:Fractional Calculus and Applied Analysis
language:en
Short-container-title:

Author:

Xu Wenjing¹,Xu Wei¹,Lu Kai²

Affiliation:

1. School of Science , Northwestern Polytechnical University , West Youyi Road, ADD 127 , Xi’an , 710129 , China

2. School of Mathematics , South China University of Technology , Wushan Road, ADD 381 , Guangzhou , 510640 , China

Abstract

Abstract This paper presents an averaging principle for fractional stochastic differential equations in ℝ n with fractional order 0 < α < 1. We obtain a time-averaged equation under suitable conditions, such that the solutions to original fractional equation can be approximated by solutions to simpler averaged equation. By mathematical manipulations, we show that the mild solution of two equations before and after averaging are equivalent in the sense of mean square, which means the classical Khasminskii approach for the integer order systems can be extended to fractional systems.

Publisher

Walter de Gruyter GmbH

Subject

Applied Mathematics,Analysis

Link

https://www.degruyter.com/document/doi/10.1515/fca-2020-0046/pdf

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