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On a Class of Distribution Dependent Stochastic Differential Equations Driven by Time-Changed Brownian Motions

Guangjun Shen, Tingting Zhang, Jie Song, Jiang-lun Wu

Applied Mathematics and Optimization, Volume: 88, Issue: 2

Swansea University Author: Jiang-lun Wu

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DOI (Published version): 10.1007/s00245-023-10007-3

Abstract

In this paper, a class of distribution dependent stochastic differential equations driven by time-changed Brownian motion is studied. The existence and uniqueness theorem of strong solutions for the distribution dependent stochastic differential equations is established. Then, sufficient conditions...

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Published in: Applied Mathematics and Optimization
ISSN: 0095-4616 1432-0606
Published: Springer Science and Business Media LLC 2023
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URI: https://cronfa.swan.ac.uk/Record/cronfa62689
first_indexed 2023-02-19T19:03:06Z
last_indexed 2024-11-14T12:21:25Z
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spelling 2024-07-29T15:07:03.1612797 v2 62689 2023-02-19 On a Class of Distribution Dependent Stochastic Differential Equations Driven by Time-Changed Brownian Motions dbd67e30d59b0f32592b15b5705af885 Jiang-lun Wu Jiang-lun Wu true false 2023-02-19 In this paper, a class of distribution dependent stochastic differential equations driven by time-changed Brownian motion is studied. The existence and uniqueness theorem of strong solutions for the distribution dependent stochastic differential equations is established. Then, sufficient conditions are provided to guarantee the solutions to be stable in several different senses in terms of Lyapunov function. Finally, we show that the solutions of the distribution dependent stochastic differential equations can be approximated by solutions of the associated averaged stochastic differential equations in mean square convergence. Journal Article Applied Mathematics and Optimization 88 2 Springer Science and Business Media LLC 0095-4616 1432-0606 Distribution dependent stochastic differential equations;Time-changed Brownian motions; Stability; Averaging principle. 1 10 2023 2023-10-01 10.1007/s00245-023-10007-3 COLLEGE NANME COLLEGE CODE Swansea University Other National Natural Science Foundation of China - 12071003 2024-07-29T15:07:03.1612797 2023-02-19T18:54:31.6148048 Faculty of Science and Engineering School of Mathematics and Computer Science - Mathematics Guangjun Shen 1 Tingting Zhang 2 Jie Song 3 Jiang-lun Wu 4 62689__26623__5b576a2ab07b4872a789e3a3c55f2d7a.pdf ShenZhangSongWu Repository.pdf 2023-02-19T19:01:55.9792669 Output 353455 application/pdf Accepted Manuscript true 2024-05-31T00:00:00.0000000 true eng
title On a Class of Distribution Dependent Stochastic Differential Equations Driven by Time-Changed Brownian Motions
spellingShingle On a Class of Distribution Dependent Stochastic Differential Equations Driven by Time-Changed Brownian Motions
Jiang-lun Wu
title_short On a Class of Distribution Dependent Stochastic Differential Equations Driven by Time-Changed Brownian Motions
title_full On a Class of Distribution Dependent Stochastic Differential Equations Driven by Time-Changed Brownian Motions
title_fullStr On a Class of Distribution Dependent Stochastic Differential Equations Driven by Time-Changed Brownian Motions
title_full_unstemmed On a Class of Distribution Dependent Stochastic Differential Equations Driven by Time-Changed Brownian Motions
title_sort On a Class of Distribution Dependent Stochastic Differential Equations Driven by Time-Changed Brownian Motions
author_id_str_mv dbd67e30d59b0f32592b15b5705af885
author_id_fullname_str_mv dbd67e30d59b0f32592b15b5705af885_***_Jiang-lun Wu
author Jiang-lun Wu
author2 Guangjun Shen
Tingting Zhang
Jie Song
Jiang-lun Wu
format Journal article
container_title Applied Mathematics and Optimization
container_volume 88
container_issue 2
publishDate 2023
institution Swansea University
issn 0095-4616
1432-0606
doi_str_mv 10.1007/s00245-023-10007-3
publisher Springer Science and Business Media LLC
college_str Faculty of Science and Engineering
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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 1
active_str 0
description In this paper, a class of distribution dependent stochastic differential equations driven by time-changed Brownian motion is studied. The existence and uniqueness theorem of strong solutions for the distribution dependent stochastic differential equations is established. Then, sufficient conditions are provided to guarantee the solutions to be stable in several different senses in terms of Lyapunov function. Finally, we show that the solutions of the distribution dependent stochastic differential equations can be approximated by solutions of the associated averaged stochastic differential equations in mean square convergence.
published_date 2023-10-01T08:19:22Z
_version_ 1821392830367531008
score 11.047739

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