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Two-time-scale stochastic differential delay equations driven by multiplicative fractional Brownian noise: Averaging principle

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

Journal of Mathematical Analysis and Applications, Volume: 510, Issue: 2, Start page: 126004

Swansea University Author: Jiang-lun Wu Orcid Logo

  • Accepted version JMAA-21-1586.pdf

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DOI (Published version): 10.1016/j.jmaa.2022.126004

Abstract

The main goal of this article is to study an averaging principle for a class of two-time-scale stochastic differential delay equations in which the slow-varying process includes a multiplicative fractional Brownian noise with Hurst parameter H ∈ (12,1) and the fast-varying process is a rapidly-chang...

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Published in: Journal of Mathematical Analysis and Applications
ISSN: 0022-247X
Published: Elsevier BV 2022
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URI: https://cronfa.swan.ac.uk/Record/cronfa59044
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first_indexed 2022-01-26T14:42:59Z
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spelling 2022-10-27T12:44:39.5288118 v2 59044 2021-12-28 Two-time-scale stochastic differential delay equations driven by multiplicative fractional Brownian noise: Averaging principle dbd67e30d59b0f32592b15b5705af885 0000-0003-4568-7013 Jiang-lun Wu Jiang-lun Wu true false 2021-12-28 SMA The main goal of this article is to study an averaging principle for a class of two-time-scale stochastic differential delay equations in which the slow-varying process includes a multiplicative fractional Brownian noise with Hurst parameter H ∈ (12,1) and the fast-varying process is a rapidly-changing diffusion. We would like to emphasize that the approach proposed in this paper is based on the fact that a stochastic integral with respect to fractional Brownian motion with Hurst parameter in (12,1) can be defined as a generalized Stieltjes integral. In particular, to prove a limit theorem for the averaging principle, we will introduce a sequence of stopping times to control the size of multiplicative fractional Brownian noise. Then, inspired by the Khasminskii’s approach, an averaging principle is developed in the sense of convergence in the p-th moment uniformly in time. Journal Article Journal of Mathematical Analysis and Applications 510 2 126004 Elsevier BV 0022-247X Averaging principle; Two-time-scaleStochastic differential delay equations; Multiplicative fractional Brownian noise. 15 6 2022 2022-06-15 10.1016/j.jmaa.2022.126004 COLLEGE NANME Mathematics COLLEGE CODE SMA Swansea University 2022-10-27T12:44:39.5288118 2021-12-28T18:34:23.4707038 Faculty of Science and Engineering School of Mathematics and Computer Science - Mathematics Min Han 1 Yong Xu 2 Bin Pei 3 Jiang-lun Wu 0000-0003-4568-7013 4 59044__22087__f6f861d0f23644eda298a2deeaf41cba.pdf Accepted version JMAA-21-1586.pdf 2022-01-10T11:49:06.7839964 Output 366313 application/pdf Accepted Manuscript true 2023-01-13T00:00:00.0000000 ©2022 All rights reserved. All article content, except where otherwise noted, is licensed under a Creative Commons Attribution Non-Commercial No Derivatives License (CC-BY-NC-ND) true eng https://creativecommons.org/licenses/by-nc-nd/4.0/
title Two-time-scale stochastic differential delay equations driven by multiplicative fractional Brownian noise: Averaging principle
spellingShingle Two-time-scale stochastic differential delay equations driven by multiplicative fractional Brownian noise: Averaging principle
Jiang-lun Wu
title_short Two-time-scale stochastic differential delay equations driven by multiplicative fractional Brownian noise: Averaging principle
title_full Two-time-scale stochastic differential delay equations driven by multiplicative fractional Brownian noise: Averaging principle
title_fullStr Two-time-scale stochastic differential delay equations driven by multiplicative fractional Brownian noise: Averaging principle
title_full_unstemmed Two-time-scale stochastic differential delay equations driven by multiplicative fractional Brownian noise: Averaging principle
title_sort Two-time-scale stochastic differential delay equations driven by multiplicative fractional Brownian noise: Averaging principle
author_id_str_mv dbd67e30d59b0f32592b15b5705af885
author_id_fullname_str_mv dbd67e30d59b0f32592b15b5705af885_***_Jiang-lun Wu
author Jiang-lun Wu
author2 Min Han
Yong Xu
Bin Pei
Jiang-lun Wu
format Journal article
container_title Journal of Mathematical Analysis and Applications
container_volume 510
container_issue 2
container_start_page 126004
publishDate 2022
institution Swansea University
issn 0022-247X
doi_str_mv 10.1016/j.jmaa.2022.126004
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
document_store_str 1
active_str 0
description The main goal of this article is to study an averaging principle for a class of two-time-scale stochastic differential delay equations in which the slow-varying process includes a multiplicative fractional Brownian noise with Hurst parameter H ∈ (12,1) and the fast-varying process is a rapidly-changing diffusion. We would like to emphasize that the approach proposed in this paper is based on the fact that a stochastic integral with respect to fractional Brownian motion with Hurst parameter in (12,1) can be defined as a generalized Stieltjes integral. In particular, to prove a limit theorem for the averaging principle, we will introduce a sequence of stopping times to control the size of multiplicative fractional Brownian noise. Then, inspired by the Khasminskii’s approach, an averaging principle is developed in the sense of convergence in the p-th moment uniformly in time.
published_date 2022-06-15T04:16:02Z
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score 11.012678

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