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Convergence rate in Lp sense of tamed EM scheme for highly nonlinear neutral multiple-delay stochastic McKean–Vlasov equations

Shuaibin Gao, Qian Guo, Junhao Hu, Chenggui Yuan Orcid Logo

Journal of Computational and Applied Mathematics, Volume: 441, Start page: 115682

Swansea University Author: Chenggui Yuan Orcid Logo

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DOI (Published version): 10.1016/j.cam.2023.115682

Abstract

This paper focuses on the numerical scheme of highly nonlinear neutral multiple-delay stochastic McKean-Vlasov equation (NMSMVE) by virtue of the stochastic particle method. First, under general assumptions, the results about propagation of chaos in Lp sense are revealed, where the convergence rate...

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Published in: Journal of Computational and Applied Mathematics
ISSN: 0377-0427 1879-1778
Published: Elsevier BV 2024
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URI: https://cronfa.swan.ac.uk/Record/cronfa64991
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first_indexed 2023-11-15T08:14:12Z
last_indexed 2023-11-15T08:14:12Z
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spelling v2 64991 2023-11-15 Convergence rate in Lp sense of tamed EM scheme for highly nonlinear neutral multiple-delay stochastic McKean–Vlasov equations 22b571d1cba717a58e526805bd9abea0 0000-0003-0486-5450 Chenggui Yuan Chenggui Yuan true false 2023-11-15 SMA This paper focuses on the numerical scheme of highly nonlinear neutral multiple-delay stochastic McKean-Vlasov equation (NMSMVE) by virtue of the stochastic particle method. First, under general assumptions, the results about propagation of chaos in Lp sense are revealed, where the convergence rate loses a little due to the proof technique. Then the tamed Euler–Maruyama scheme to the corresponding particle system is established and the convergence rate in Lp sense is obtained. Furthermore, combining these two results gives the convergence error in Lp sense between the objective NMSMVE and numerical approximation, which is related to the particle number and step size. Finally, two numerical examples are provided to support the finding. Journal Article Journal of Computational and Applied Mathematics 441 115682 Elsevier BV 0377-0427 1879-1778 The tamed Euler–Maruyama scheme, Neutral multiple-delay stochastic McKean-Vlasov equation, Strong convergence rate, Propagation of chaos 15 5 2024 2024-05-15 10.1016/j.cam.2023.115682 http://dx.doi.org/10.1016/j.cam.2023.115682 COLLEGE NANME Mathematics COLLEGE CODE SMA Swansea University This work is supported by the National Natural Science Foundation of China (Grant Nos. 12271368, 11871343 and 62373383) and Shanghai Rising-Star Program, China (Grant No. 22QA1406900). 2024-01-03T17:01:32.0379389 2023-11-15T08:12:11.6033998 Faculty of Science and Engineering School of Mathematics and Computer Science - Mathematics Shuaibin Gao 1 Qian Guo 2 Junhao Hu 3 Chenggui Yuan 0000-0003-0486-5450 4 64991__29359__f3681d6bccca47e9b24ada49cfeb20a5.pdf 64991.VOR.pdf 2024-01-03T17:00:30.9409304 Output 697406 application/pdf Version of Record true © 2023 The Author(s). Published by Elsevier B.V. Distributed under the terms of a Creative Commons Attribution 4.0 International License (CC BY 4.0). true eng https://creativecommons.org/licenses/by/4.0/
title Convergence rate in Lp sense of tamed EM scheme for highly nonlinear neutral multiple-delay stochastic McKean–Vlasov equations
spellingShingle Convergence rate in Lp sense of tamed EM scheme for highly nonlinear neutral multiple-delay stochastic McKean–Vlasov equations
Chenggui Yuan
title_short Convergence rate in Lp sense of tamed EM scheme for highly nonlinear neutral multiple-delay stochastic McKean–Vlasov equations
title_full Convergence rate in Lp sense of tamed EM scheme for highly nonlinear neutral multiple-delay stochastic McKean–Vlasov equations
title_fullStr Convergence rate in Lp sense of tamed EM scheme for highly nonlinear neutral multiple-delay stochastic McKean–Vlasov equations
title_full_unstemmed Convergence rate in Lp sense of tamed EM scheme for highly nonlinear neutral multiple-delay stochastic McKean–Vlasov equations
title_sort Convergence rate in Lp sense of tamed EM scheme for highly nonlinear neutral multiple-delay stochastic McKean–Vlasov equations
author_id_str_mv 22b571d1cba717a58e526805bd9abea0
author_id_fullname_str_mv 22b571d1cba717a58e526805bd9abea0_***_Chenggui Yuan
author Chenggui Yuan
author2 Shuaibin Gao
Qian Guo
Junhao Hu
Chenggui Yuan
format Journal article
container_title Journal of Computational and Applied Mathematics
container_volume 441
container_start_page 115682
publishDate 2024
institution Swansea University
issn 0377-0427
1879-1778
doi_str_mv 10.1016/j.cam.2023.115682
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.cam.2023.115682
document_store_str 1
active_str 0
description This paper focuses on the numerical scheme of highly nonlinear neutral multiple-delay stochastic McKean-Vlasov equation (NMSMVE) by virtue of the stochastic particle method. First, under general assumptions, the results about propagation of chaos in Lp sense are revealed, where the convergence rate loses a little due to the proof technique. Then the tamed Euler–Maruyama scheme to the corresponding particle system is established and the convergence rate in Lp sense is obtained. Furthermore, combining these two results gives the convergence error in Lp sense between the objective NMSMVE and numerical approximation, which is related to the particle number and step size. Finally, two numerical examples are provided to support the finding.
published_date 2024-05-15T17:01:33Z
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score 11.016235

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