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Asymptotic behaviors for distribution dependent SDEs driven by fractional Brownian motions

Xiliang Fan, Ting Yu, Chenggui Yuan Orcid Logo

Stochastic Processes and their Applications, Volume: 164, Pages: 383 - 415

Swansea University Author: Chenggui Yuan Orcid Logo

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DOI (Published version): 10.1016/j.spa.2023.07.015

Abstract

In this paper, we study small-noise asymptotic behaviors for a class of distribution dependent stochastic differential equations driven by fractional Brownian motions with Hurst parameter H ∈ (1/2, 1) and magnitude ϵH. By building up a variational framework and two weak convergence criteria in the f...

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Published in: Stochastic Processes and their Applications
ISSN: 0304-4149
Published: Elsevier BV 2023
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URI: https://cronfa.swan.ac.uk/Record/cronfa63996
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last_indexed 2023-07-31T08:13:36Z
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spelling v2 63996 2023-07-31 Asymptotic behaviors for distribution dependent SDEs driven by fractional Brownian motions 22b571d1cba717a58e526805bd9abea0 0000-0003-0486-5450 Chenggui Yuan Chenggui Yuan true false 2023-07-31 SMA In this paper, we study small-noise asymptotic behaviors for a class of distribution dependent stochastic differential equations driven by fractional Brownian motions with Hurst parameter H ∈ (1/2, 1) and magnitude ϵH. By building up a variational framework and two weak convergence criteria in the factional Brownian motion setting, we establish the large and moderate deviation principles for these types of equations. Besides, we also obtain the central limit theorem, in which the limit process solves a linear equation involving the Lions derivative of the drift coefficient. Journal Article Stochastic Processes and their Applications 164 383 415 Elsevier BV 0304-4149 Distribution dependent SDE, Fractional Brownian motion, Large deviation principle, Moderate deviation principle, Central limit theorem 1 10 2023 2023-10-01 10.1016/j.spa.2023.07.015 http://dx.doi.org/10.1016/j.spa.2023.07.015 COLLEGE NANME Mathematics COLLEGE CODE SMA Swansea University SU Library paid the OA fee (TA Institutional Deal) Swansea University 2023-09-07T13:33:52.7347177 2023-07-31T09:09:54.9555087 Faculty of Science and Engineering School of Mathematics and Computer Science - Mathematics Xiliang Fan 1 Ting Yu 2 Chenggui Yuan 0000-0003-0486-5450 3 63996__28316__5fbc39adc5084c6cae6ed838720ed749.pdf 63996.VOR.pdf 2023-08-18T11:55:54.6238965 Output 1805811 application/pdf Version of Record true © 2023 The Author(s). This is an open access article under the CCBY-NC-ND license. true eng http://creativecommons.org/licenses/by-nc-nd/4.0/
title Asymptotic behaviors for distribution dependent SDEs driven by fractional Brownian motions
spellingShingle Asymptotic behaviors for distribution dependent SDEs driven by fractional Brownian motions
Chenggui Yuan
title_short Asymptotic behaviors for distribution dependent SDEs driven by fractional Brownian motions
title_full Asymptotic behaviors for distribution dependent SDEs driven by fractional Brownian motions
title_fullStr Asymptotic behaviors for distribution dependent SDEs driven by fractional Brownian motions
title_full_unstemmed Asymptotic behaviors for distribution dependent SDEs driven by fractional Brownian motions
title_sort Asymptotic behaviors for distribution dependent SDEs driven by fractional Brownian motions
author_id_str_mv 22b571d1cba717a58e526805bd9abea0
author_id_fullname_str_mv 22b571d1cba717a58e526805bd9abea0_***_Chenggui Yuan
author Chenggui Yuan
author2 Xiliang Fan
Ting Yu
Chenggui Yuan
format Journal article
container_title Stochastic Processes and their Applications
container_volume 164
container_start_page 383
publishDate 2023
institution Swansea University
issn 0304-4149
doi_str_mv 10.1016/j.spa.2023.07.015
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.spa.2023.07.015
document_store_str 1
active_str 0
description In this paper, we study small-noise asymptotic behaviors for a class of distribution dependent stochastic differential equations driven by fractional Brownian motions with Hurst parameter H ∈ (1/2, 1) and magnitude ϵH. By building up a variational framework and two weak convergence criteria in the factional Brownian motion setting, we establish the large and moderate deviation principles for these types of equations. Besides, we also obtain the central limit theorem, in which the limit process solves a linear equation involving the Lions derivative of the drift coefficient.
published_date 2023-10-01T13:33:54Z
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score 11.013731

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