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Abstract and Applied Analysis
Volume 2014 (2014), Article ID 479195, 10 pages
http://dx.doi.org/10.1155/2014/479195
Research Article

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

Department of Applied Mathematics, Northwestern Polytechnical University, Xi’an 710072, China

Received 15 November 2013; Accepted 19 December 2013; Published 22 January 2014

Academic Editor: Yaozhong Hu

Copyright © 2014 Yong Xu et al. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

Abstract

An averaging principle for a class of stochastic differential delay equations (SDDEs) driven by fractional Brownian motion (fBm) with Hurst parameter in 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.