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Stochastic averaging for stochastic differential equations driven by fractional Brownian motion and standard Brownian motion

Bin Pei, Yong Xu, Jiang-lun Wu Orcid Logo

Applied Mathematics Letters, Volume: 100, Start page: 106006

Swansea University Author: Jiang-lun Wu Orcid Logo

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DOI (Published version): 10.1016/j.aml.2019.106006

Abstract

In this paper, an averaging principle for multidimensional, time dependent, stochastic differential equations (SDEs) driven by fractional Brownian motion and standard Brownian motion was established. We combined the pathwise approach with the Itˆo stochastic calculus to handle both types of integral...

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Published in: Applied Mathematics Letters
ISSN: 0893-9659
Published: Elsevier BV 2020
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URI: https://cronfa.swan.ac.uk/Record/cronfa51701
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first_indexed 2019-09-05T20:44:23Z
last_indexed 2019-09-21T20:18:24Z
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spelling 2019-09-21T16:32:42.8614786 v2 51701 2019-09-05 Stochastic averaging for stochastic differential equations driven by fractional Brownian motion and standard Brownian motion dbd67e30d59b0f32592b15b5705af885 0000-0003-4568-7013 Jiang-lun Wu Jiang-lun Wu true false 2019-09-05 SMA In this paper, an averaging principle for multidimensional, time dependent, stochastic differential equations (SDEs) driven by fractional Brownian motion and standard Brownian motion was established. We combined the pathwise approach with the Itˆo stochastic calculus to handle both types of integrals involved and proved that the original SDEs can be approximated by averaged SDEs in the manner of mean square convergence and of convergence in probability, respectively. Journal Article Applied Mathematics Letters 100 106006 Elsevier BV 0893-9659 Averaging principle, fractional Brownian motion, pathwise Riemann-Stieltjes integral, Itˆo stochastic calculus. 28 2 2020 2020-02-28 10.1016/j.aml.2019.106006 http://dx.doi.org/10.1016/j.aml.2019.106006 COLLEGE NANME Mathematics COLLEGE CODE SMA Swansea University COAF,RCUK,Institution 2019-09-21T16:32:42.8614786 2019-09-05T15:48:44.0941047 Faculty of Science and Engineering School of Mathematics and Computer Science - Mathematics Bin Pei 1 Yong Xu 2 Jiang-lun Wu 0000-0003-4568-7013 3 51701__15342__8ca6dc37fd9d48feba54001da03aa48f.pdf pei-xu-wu.pdf 2019-09-21T16:32:25.3470000 Output 273164 application/pdf Accepted Manuscript true 2020-08-19T00:00:00.0000000 true eng
title Stochastic averaging for stochastic differential equations driven by fractional Brownian motion and standard Brownian motion
spellingShingle Stochastic averaging for stochastic differential equations driven by fractional Brownian motion and standard Brownian motion
Jiang-lun Wu
title_short Stochastic averaging for stochastic differential equations driven by fractional Brownian motion and standard Brownian motion
title_full Stochastic averaging for stochastic differential equations driven by fractional Brownian motion and standard Brownian motion
title_fullStr Stochastic averaging for stochastic differential equations driven by fractional Brownian motion and standard Brownian motion
title_full_unstemmed Stochastic averaging for stochastic differential equations driven by fractional Brownian motion and standard Brownian motion
title_sort Stochastic averaging for stochastic differential equations driven by fractional Brownian motion and standard Brownian motion
author_id_str_mv dbd67e30d59b0f32592b15b5705af885
author_id_fullname_str_mv dbd67e30d59b0f32592b15b5705af885_***_Jiang-lun Wu
author Jiang-lun Wu
author2 Bin Pei
Yong Xu
Jiang-lun Wu
format Journal article
container_title Applied Mathematics Letters
container_volume 100
container_start_page 106006
publishDate 2020
institution Swansea University
issn 0893-9659
doi_str_mv 10.1016/j.aml.2019.106006
publisher Elsevier BV
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
url http://dx.doi.org/10.1016/j.aml.2019.106006
document_store_str 1
active_str 0
description In this paper, an averaging principle for multidimensional, time dependent, stochastic differential equations (SDEs) driven by fractional Brownian motion and standard Brownian motion was established. We combined the pathwise approach with the Itˆo stochastic calculus to handle both types of integrals involved and proved that the original SDEs can be approximated by averaged SDEs in the manner of mean square convergence and of convergence in probability, respectively.
published_date 2020-02-28T04:03:42Z
_version_ 1763753300020166656
score 11.012678

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