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A strong averaging principle rate for two-time-scale coupled forward-backward stochastic differential equations driven by fractional Brownian motion

Jie Xu, Qiqi Lian, Jiang-lun Wu

Applied Mathematics and Optimization, Volume: 88, Issue: 32

Swansea University Author: Jiang-lun Wu

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DOI (Published version): 10.1007/s00245-023-10008-2

Abstract

This paper concerns the strong convergence rate of an averaging principle for two- time-scale forward-backward stochastic differential equations (FBSDEs, for short) driven by fractional Brownian motion (fBm, for short). The fast component is driven by Brownian motion, while the slow component is dri...

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Published in: Applied Mathematics and Optimization
ISSN: 0095-4616 1432-0606
Published: Springer
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URI: https://cronfa.swan.ac.uk/Record/cronfa63257
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first_indexed 2023-04-26T20:08:31Z
last_indexed 2023-04-26T20:08:31Z
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spelling v2 63257 2023-04-26 A strong averaging principle rate for two-time-scale coupled forward-backward stochastic differential equations driven by fractional Brownian motion dbd67e30d59b0f32592b15b5705af885 Jiang-lun Wu Jiang-lun Wu true false 2023-04-26 FGSEN This paper concerns the strong convergence rate of an averaging principle for two- time-scale forward-backward stochastic differential equations (FBSDEs, for short) driven by fractional Brownian motion (fBm, for short). The fast component is driven by Brownian motion, while the slow component is driven by fBm with the Hurst index greater than 1/2. Combining Malliavin calculus theory to stochastic integral and Khasminskii’s time discretization method, the rate of strong convergence for the slow component towards the solution of the averaging equation in the mean square sense is derived. The averaging principle for fast-slow FBSDEs driven by fBm is new. Journal Article Applied Mathematics and Optimization 88 32 Springer 0095-4616 1432-0606 Stochastic averaging principle, Convergence rate, Fractional Brownian motion, Fast–slow forward–backward stochastic differential equations 0 0 0 0001-01-01 10.1007/s00245-023-10008-2 COLLEGE NANME Science and Engineering - Faculty COLLEGE CODE FGSEN Swansea University Other 2023-06-30T14:48:38.6767593 2023-04-26T20:58:33.9636653 Faculty of Science and Engineering School of Mathematics and Computer Science - Mathematics Jie Xu 1 Qiqi Lian 2 Jiang-lun Wu 3 Under embargo Under embargo 2023-04-26T21:07:17.7973416 Output 409543 application/pdf Accepted Manuscript true 2024-05-31T00:00:00.0000000 true eng
title A strong averaging principle rate for two-time-scale coupled forward-backward stochastic differential equations driven by fractional Brownian motion
spellingShingle A strong averaging principle rate for two-time-scale coupled forward-backward stochastic differential equations driven by fractional Brownian motion
Jiang-lun Wu
title_short A strong averaging principle rate for two-time-scale coupled forward-backward stochastic differential equations driven by fractional Brownian motion
title_full A strong averaging principle rate for two-time-scale coupled forward-backward stochastic differential equations driven by fractional Brownian motion
title_fullStr A strong averaging principle rate for two-time-scale coupled forward-backward stochastic differential equations driven by fractional Brownian motion
title_full_unstemmed A strong averaging principle rate for two-time-scale coupled forward-backward stochastic differential equations driven by fractional Brownian motion
title_sort A strong averaging principle rate for two-time-scale coupled forward-backward stochastic differential equations driven by fractional Brownian motion
author_id_str_mv dbd67e30d59b0f32592b15b5705af885
author_id_fullname_str_mv dbd67e30d59b0f32592b15b5705af885_***_Jiang-lun Wu
author Jiang-lun Wu
author2 Jie Xu
Qiqi Lian
Jiang-lun Wu
format Journal article
container_title Applied Mathematics and Optimization
container_volume 88
container_issue 32
institution Swansea University
issn 0095-4616
1432-0606
doi_str_mv 10.1007/s00245-023-10008-2
publisher Springer
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 0
active_str 0
description This paper concerns the strong convergence rate of an averaging principle for two- time-scale forward-backward stochastic differential equations (FBSDEs, for short) driven by fractional Brownian motion (fBm, for short). The fast component is driven by Brownian motion, while the slow component is driven by fBm with the Hurst index greater than 1/2. Combining Malliavin calculus theory to stochastic integral and Khasminskii’s time discretization method, the rate of strong convergence for the slow component towards the solution of the averaging equation in the mean square sense is derived. The averaging principle for fast-slow FBSDEs driven by fBm is new.
published_date 0001-01-01T14:48:34Z
_version_ 1770135659349016576
score 11.012678

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