AN AVERAGING PRINCIPLE FOR STOCHASTIC DIFFERENTIAL EQUATIONS OF FRACTIONAL ORDER 0 < α < 1

被引：18

作者：

Xu, Wenjing ^{[1
]}

Xu, Wei ^{[1
]}

Lu, Kai ^{[2
]}

机构：

[1] Northwestern Polytech Univ, Sch Sci, West Youyi Rd,ADD 127, Xian 710129, Peoples R China

[2] South China Univ Technol, Sch Math, Wushan Rd,ADD 381, Guangzhou 510640, Peoples R China

来源：

FRACTIONAL CALCULUS AND APPLIED ANALYSIS | 2020年 / 23卷 / 03期

基金：

中国国家自然科学基金;

关键词：

averaging principle; fractional derivative; stochastic differential equations; DIFFUSION;

D O I：

10.1515/fca-2020-0046

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

This paper presents an averaging principle for fractional stochastic differential equations in R-n with fractional order 0 < alpha < 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.

引用

页码：908 / 919

页数：12

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AN AVERAGING PRINCIPLE FOR STOCHASTIC DIFFERENTIAL EQUATIONS OF FRACTIONAL ORDER 0 &lt; α &lt; 1

AN AVERAGING PRINCIPLE FOR STOCHASTIC DIFFERENTIAL EQUATIONS OF FRACTIONAL ORDER 0 < α < 1