Status | 已发表Published |
Title | Stochastic averaging principle for differential equations with non-Lipschitz coefficients driven by fractional Brownian motion |
Creator | |
Date Issued | 2017-04-01 |
Source Publication | Stochastics and Dynamics
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ISSN | 0219-4937 |
Volume | 17Issue: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. |
Keyword | fractional Brownian motion non-Lipschitz coefficients pathwise integrals stochastic averaging Stochastic differential equations |
DOI | 10.1142/S0219493717500137 |
URL | View source |
Indexed By | SCIE |
Language | 英语English |
WOS Research Area | Mathematics |
WOS Subject | Statistics & Probability |
WOS ID | WOS:000398859100005 |
Scopus ID | 2-s2.0-85016177109 |
Citation statistics | |
Document Type | Journal article |
Identifier | http://repository.uic.edu.cn/handle/39GCC9TT/10508 |
Collection | Research outside affiliated institution |
Corresponding Author | Xu, 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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