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Status已发表Published
TitleStochastic averaging principle for differential equations with non-Lipschitz coefficients driven by fractional Brownian motion
Creator
Date Issued2017-04-01
Source PublicationStochastics and Dynamics
ISSN0219-4937
Volume17Issue:2
Abstract

In this paper, we are concerned with the stochastic averaging principle for stochastic differential equations (SDEs) with non-Lipschitz coefficients driven by fractional Brownian motion (fBm) of the Hurst parameter H ∈(1/2, 1). We define the stochastic integrals with respect to the fBm in the integral formulation of the SDEs as pathwise integrals and we adopt the non-Lipschitz condition proposed by Taniguchi (1992) which is a much weaker condition with wider range of applications. The averaged SDEs are established. We then use their corresponding solutions to approximate the solutions of the original SDEs both in the sense of mean square and of probability. One can find that the similar asymptotic results are suitable for those non-Lipschitz SDEs with fBm under different types of stochastic integrals.

Keywordfractional Brownian motion non-Lipschitz coefficients pathwise integrals stochastic averaging Stochastic differential equations
DOI10.1142/S0219493717500137
URLView source
Indexed BySCIE
Language英语English
WOS Research AreaMathematics
WOS SubjectStatistics & Probability
WOS IDWOS:000398859100005
Scopus ID2-s2.0-85016177109
Citation statistics
Cited Times:75[WOS]   [WOS Record]     [Related Records in WOS]
Document TypeJournal article
Identifierhttp://repository.uic.edu.cn/handle/39GCC9TT/10508
CollectionResearch outside affiliated institution
Corresponding AuthorXu, Yong
Affiliation
1.Department of Applied Mathematics,Northwestern Polytechnical University,Xi'an,710072,China
2.Department of Mathematics,Swansea University,Swansea,SA2 8PP,United Kingdom
Recommended Citation
GB/T 7714
Xu, Yong,Pei, Bin,Wu, Jianglun. Stochastic averaging principle for differential equations with non-Lipschitz coefficients driven by fractional Brownian motion[J]. Stochastics and Dynamics, 2017, 17(2).
APA Xu, Yong, Pei, Bin, & Wu, Jianglun. (2017). Stochastic averaging principle for differential equations with non-Lipschitz coefficients driven by fractional Brownian motion. Stochastics and Dynamics, 17(2).
MLA Xu, Yong,et al."Stochastic averaging principle for differential equations with non-Lipschitz coefficients driven by fractional Brownian motion". Stochastics and Dynamics 17.2(2017).
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