## Abstract and Applied Analysis

### An Averaging Principle for Stochastic Differential Delay Equations with Fractional Brownian Motion

Yong Xu, Bin Pei, and Yongge Li

#### Abstract

An averaging principle for a class of stochastic differential delay equations (SDDEs) driven by fractional Brownian motion (fBm) with Hurst parameter in $(\mathrm{1}/\mathrm{2},\mathrm{1})$ is considered, where stochastic integration is convolved as the path integrals. The solutions to the original SDDEs can be approximated by solutions to the corresponding averaged SDDEs in the sense of both convergence in mean square and in probability, respectively. Two examples are carried out to illustrate the proposed averaging principle.

#### Article information

Source
Abstr. Appl. Anal., Volume 2014, Special Issue (2013), Article ID 479195, 10 pages.

Dates
First available in Project Euclid: 26 March 2014

Permanent link to this document
https://projecteuclid.org/euclid.aaa/1395858397

Digital Object Identifier
doi:10.1155/2014/479195

Mathematical Reviews number (MathSciNet)
MR3166618

Zentralblatt MATH identifier
07022457

#### Citation

Xu, Yong; Pei, Bin; Li, Yongge. An Averaging Principle for Stochastic Differential Delay Equations with Fractional Brownian Motion. Abstr. Appl. Anal. 2014, Special Issue (2013), Article ID 479195, 10 pages. doi:10.1155/2014/479195. https://projecteuclid.org/euclid.aaa/1395858397

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