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

An averaging principle for a class of stochastic differential delay equations (SDDEs) driven by fractional Brownian motion (fBm) with Hurst parameter in ( 1 / 2 , 1 ) is considered, where stochastic integration is convolved as the path integrals. The solutions to the original SDDEs can be approximat...

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Bibliographic Details
Published inAbstract and Applied Analysis Vol. 2014; no. 2014; pp. 214 - 223-722
Main Authors Xu, Yong, Li, Yongge, Pei, Bin
Format Journal Article
LanguageEnglish
Published Cairo, Egypt Hindawi Limiteds 01.01.2014
Hindawi Publishing Corporation
Hindawi Limited
Wiley
Subjects
Applied mathematics
Brownian motion
Delay equations
Differential equations
Hilbert space
Mathematical research
Random variables
Stochastic differential equations
Stochastic models
Studies
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Summary:An averaging principle for a class of stochastic differential delay equations (SDDEs) driven by fractional Brownian motion (fBm) with Hurst parameter in ( 1 / 2 , 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.
ISSN:1085-3375
1687-0409
DOI:10.1155/2014/479195