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Stochastic averaging principle for differential equations with non-Lipschitz coefficients driven by fractional Brownian motion

Yong Xu, Bin Pei, Jiang-lun Wu

Stochastics and Dynamics, Start page: 1750013

Swansea University Author: Jiang-lun Wu

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DOI (Published version): 10.1142/S0219493717500137

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 , 1). We define the stochastic integrals with respect to the fBm in the integ...

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Published in: Stochastics and Dynamics
ISSN: 1793-6799
Published: 2017
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URI: https://cronfa.swan.ac.uk/Record/cronfa28501
first_indexed 2016-06-02T18:23:42Z
last_indexed 2018-02-09T05:12:41Z
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spelling 2017-06-28T17:17:21.6638050 v2 28501 2016-06-02 Stochastic averaging principle for differential equations with non-Lipschitz coefficients driven by fractional Brownian motion dbd67e30d59b0f32592b15b5705af885 Jiang-lun Wu Jiang-lun Wu true false 2016-06-02 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 , 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. Journal Article Stochastics and Dynamics 1750013 1793-6799 Stochastic differential equations; non-Lipschitz coefficients; fractional Brow- nian motion; stochastic averaging; pathwise integrals. 3 4 2017 2017-04-03 10.1142/S0219493717500137 COLLEGE NANME COLLEGE CODE Swansea University 2017-06-28T17:17:21.6638050 2016-06-02T17:01:14.4867488 Faculty of Science and Engineering School of Mathematics and Computer Science - Mathematics Yong Xu 1 Bin Pei 2 Jiang-lun Wu 3
title Stochastic averaging principle for differential equations with non-Lipschitz coefficients driven by fractional Brownian motion
spellingShingle Stochastic averaging principle for differential equations with non-Lipschitz coefficients driven by fractional Brownian motion
Jiang-lun Wu
title_short Stochastic averaging principle for differential equations with non-Lipschitz coefficients driven by fractional Brownian motion
title_full Stochastic averaging principle for differential equations with non-Lipschitz coefficients driven by fractional Brownian motion
title_fullStr Stochastic averaging principle for differential equations with non-Lipschitz coefficients driven by fractional Brownian motion
title_full_unstemmed Stochastic averaging principle for differential equations with non-Lipschitz coefficients driven by fractional Brownian motion
title_sort Stochastic averaging principle for differential equations with non-Lipschitz coefficients driven by fractional Brownian motion
author_id_str_mv dbd67e30d59b0f32592b15b5705af885
author_id_fullname_str_mv dbd67e30d59b0f32592b15b5705af885_***_Jiang-lun Wu
author Jiang-lun Wu
author2 Yong Xu
Bin Pei
Jiang-lun Wu
format Journal article
container_title Stochastics and Dynamics
container_start_page 1750013
publishDate 2017
institution Swansea University
issn 1793-6799
doi_str_mv 10.1142/S0219493717500137
college_str Faculty of Science and Engineering
hierarchytype
hierarchy_top_id facultyofscienceandengineering
hierarchy_top_title Faculty of Science and Engineering
hierarchy_parent_id facultyofscienceandengineering
hierarchy_parent_title Faculty of Science and Engineering
department_str School of Mathematics and Computer Science - Mathematics{{{_:::_}}}Faculty of Science and Engineering{{{_:::_}}}School of Mathematics and Computer Science - Mathematics
document_store_str 0
active_str 0
description 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 , 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.
published_date 2017-04-03T18:56:48Z
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score 11.04748

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