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Averaging principle for distribution dependent stochastic differential equations driven by fractional Brownian motion and standard Brownian motion

Guangjun Shen, Jie Xiang Orcid Logo, Jiang-lun Wu Orcid Logo

Journal of Differential Equations, Volume: 321, Pages: 381 - 414

Swansea University Author: Jiang-lun Wu Orcid Logo

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DOI (Published version): 10.1016/j.jde.2022.03.015

Abstract

In this paper, we study distribution dependent stochastic differential equations driven simultaneously by fractional Brownian motion with Hurst index H > 1/2 and standard Brownian motion. We first establish the existence and uniqueness theorem for solutions of the distribution dependent stochasti...

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Published in: Journal of Differential Equations
ISSN: 0022-0396
Published: Elsevier BV 2022
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URI: https://cronfa.swan.ac.uk/Record/cronfa59426
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first_indexed 2022-02-20T23:48:23Z
last_indexed 2023-01-11T14:40:41Z
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spelling 2022-11-08T15:38:37.2241459 v2 59426 2022-02-20 Averaging principle for distribution dependent 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 2022-02-20 SMA In this paper, we study distribution dependent stochastic differential equations driven simultaneously by fractional Brownian motion with Hurst index H > 1/2 and standard Brownian motion. We first establish the existence and uniqueness theorem for solutions of the distribution dependent stochastic differential equations by utilising the Carath\'eodory approximation. We then show that, under certain averaging condition, the solutions of distribution dependent stochastic differential equations can be approximated by the solutions of the associated averaged distribution dependent stochastic differential equations in the sense of the mean square convergence. Journal Article Journal of Differential Equations 321 381 414 Elsevier BV 0022-0396 Distribution dependent stochastic differential equations; fractional Brow- nian motion; stochastic averaging principle. 1 6 2022 2022-06-01 10.1016/j.jde.2022.03.015 http://dx.doi.org/10.1016/j.jde.2022.03.015 COLLEGE NANME Mathematics COLLEGE CODE SMA Swansea University Not Required 2022-11-08T15:38:37.2241459 2022-02-20T23:36:35.0796369 Faculty of Science and Engineering School of Mathematics and Computer Science - Mathematics Guangjun Shen 1 Jie Xiang 0000-0001-6165-5498 2 Jiang-lun Wu 0000-0003-4568-7013 3 59426__22410__48e5b12a62474f698c4a906ca1357127.pdf ShenXiangWu.pdf 2022-02-20T23:45:23.1616311 Output 337777 application/pdf Accepted Manuscript true 2023-03-17T00:00:00.0000000 true eng https://creativecommons.org/licenses/by-nd/4.0/
title Averaging principle for distribution dependent stochastic differential equations driven by fractional Brownian motion and standard Brownian motion
spellingShingle Averaging principle for distribution dependent stochastic differential equations driven by fractional Brownian motion and standard Brownian motion
Jiang-lun Wu
title_short Averaging principle for distribution dependent stochastic differential equations driven by fractional Brownian motion and standard Brownian motion
title_full Averaging principle for distribution dependent stochastic differential equations driven by fractional Brownian motion and standard Brownian motion
title_fullStr Averaging principle for distribution dependent stochastic differential equations driven by fractional Brownian motion and standard Brownian motion
title_full_unstemmed Averaging principle for distribution dependent stochastic differential equations driven by fractional Brownian motion and standard Brownian motion
title_sort Averaging principle for distribution dependent 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 Guangjun Shen
Jie Xiang
Jiang-lun Wu
format Journal article
container_title Journal of Differential Equations
container_volume 321
container_start_page 381
publishDate 2022
institution Swansea University
issn 0022-0396
doi_str_mv 10.1016/j.jde.2022.03.015
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.jde.2022.03.015
document_store_str 1
active_str 0
description In this paper, we study distribution dependent stochastic differential equations driven simultaneously by fractional Brownian motion with Hurst index H > 1/2 and standard Brownian motion. We first establish the existence and uniqueness theorem for solutions of the distribution dependent stochastic differential equations by utilising the Carath\'eodory approximation. We then show that, under certain averaging condition, the solutions of distribution dependent stochastic differential equations can be approximated by the solutions of the associated averaged distribution dependent stochastic differential equations in the sense of the mean square convergence.
published_date 2022-06-01T04:16:43Z
_version_ 1763754119013597184
score 11.037056

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