Euler–Maruyama scheme for delay-type stochastic McKean-Vlasov equations driven by fractional Brownian motion

Gao, Shuaibin; Guo, Qian; Liu, Zhuoqi; Yuan, Chenggui

doi:10.1016/j.cnsns.2025.108927

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Euler–Maruyama scheme for delay-type stochastic McKean-Vlasov equations driven by fractional Brownian motion

Shuaibin Gao, Qian Guo, Zhuoqi Liu, Chenggui Yuan

Communications in Nonlinear Science and Numerical Simulation, Volume: 149, Start page: 108927

Swansea University Author: Chenggui Yuan

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DOI (Published version): 10.1016/j.cnsns.2025.108927

Abstract

This paper focuses on the Euler-Maruyama (EM) scheme for delay-type stochastic McKean-Vlasov equations (DSMVEs) driven by fractional Brownian motion with Hurst parameter H ∈ (0, 1/2) ∪ (1/2, 1). The existence and uniqueness of the solutions to such DSMVEs whose drift coefficients contain polynomial...

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Published in:	Communications in Nonlinear Science and Numerical Simulation
ISSN:	1007-5704 1878-7274
Published:	Elsevier BV 2025
Online Access:	Check full text
URI:	https://cronfa.swan.ac.uk/Record/cronfa69505

first_indexed	2025-05-14T09:24:47Z
last_indexed	2025-06-11T08:22:42Z
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spelling	2025-06-10T14:52:54.3426008 v2 69505 2025-05-14 Euler–Maruyama scheme for delay-type stochastic McKean-Vlasov equations driven by fractional Brownian motion 22b571d1cba717a58e526805bd9abea0 0000-0003-0486-5450 Chenggui Yuan Chenggui Yuan true false 2025-05-14 MACS This paper focuses on the Euler-Maruyama (EM) scheme for delay-type stochastic McKean-Vlasov equations (DSMVEs) driven by fractional Brownian motion with Hurst parameter H ∈ (0, 1/2) ∪ (1/2, 1). The existence and uniqueness of the solutions to such DSMVEs whose drift coefficients contain polynomial delay terms are proved by exploiting the Banach fixed point theorem. Then thepropagation of chaos between interacting particle system and non-interacting system in Lp sense is shown. We find that even if the delay term satisfies the polynomial growth condition, the unmodified classical EM scheme still can approximate the corresponding interacting particle system without the particle corruption. The convergence rates are revealed for H ∈ (0, 1/2) ∪ (1/2, 1). Finally, as an example that closely fits the original equation, a stochastic opinion dynamics model with both extrinsic memory and intrinsic memory is simulated to illustrate the plausibility of the theoretical result. Journal Article Communications in Nonlinear Science and Numerical Simulation 149 108927 Elsevier BV 1007-5704 1878-7274 Delay-type stochastic mcKean-vlasov equations; Fractional brownian motion; Propagation of chaos; Euler–maruyama scheme; Strong convergence rate 1 10 2025 2025-10-01 10.1016/j.cnsns.2025.108927 COLLEGE NANME Mathematics and Computer Science School COLLEGE CODE MACS Swansea University SU Library paid the OA fee (TA Institutional Deal) This work is supported by the National Natural Science Foundation of China (12271368, 62373383 and 62076106) and Fund for Academic Innovation Teams of South-Central Minzu University (XTZ24004). 2025-06-10T14:52:54.3426008 2025-05-14T09:36:52.0186186 Faculty of Science and Engineering School of Mathematics and Computer Science - Mathematics Shuaibin Gao 1 Qian Guo 2 Zhuoqi Liu 3 Chenggui Yuan 0000-0003-0486-5450 4 69505__34453__357bb2c96b6a484285d25d9fcd53a3a0.pdf 69505.VOR.pdf 2025-06-10T14:50:20.9148687 Output 1583634 application/pdf Version of Record true © 2025 The Authors. This is an open access article distributed under the terms of the Creative Commons CC-BY license. true eng http://creativecommons.org/licenses/by/4.0/
title	Euler–Maruyama scheme for delay-type stochastic McKean-Vlasov equations driven by fractional Brownian motion
spellingShingle	Euler–Maruyama scheme for delay-type stochastic McKean-Vlasov equations driven by fractional Brownian motion Chenggui Yuan
title_short	Euler–Maruyama scheme for delay-type stochastic McKean-Vlasov equations driven by fractional Brownian motion
title_full	Euler–Maruyama scheme for delay-type stochastic McKean-Vlasov equations driven by fractional Brownian motion
title_fullStr	Euler–Maruyama scheme for delay-type stochastic McKean-Vlasov equations driven by fractional Brownian motion
title_full_unstemmed	Euler–Maruyama scheme for delay-type stochastic McKean-Vlasov equations driven by fractional Brownian motion
title_sort	Euler–Maruyama scheme for delay-type stochastic McKean-Vlasov equations driven by fractional Brownian motion
author_id_str_mv	22b571d1cba717a58e526805bd9abea0
author_id_fullname_str_mv	22b571d1cba717a58e526805bd9abea0_***_Chenggui Yuan
author	Chenggui Yuan
author2	Shuaibin Gao Qian Guo Zhuoqi Liu Chenggui Yuan
format	Journal article
container_title	Communications in Nonlinear Science and Numerical Simulation
container_volume	149
container_start_page	108927
publishDate	2025
institution	Swansea University
issn	1007-5704 1878-7274
doi_str_mv	10.1016/j.cnsns.2025.108927
publisher	Elsevier BV
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
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description	This paper focuses on the Euler-Maruyama (EM) scheme for delay-type stochastic McKean-Vlasov equations (DSMVEs) driven by fractional Brownian motion with Hurst parameter H ∈ (0, 1/2) ∪ (1/2, 1). The existence and uniqueness of the solutions to such DSMVEs whose drift coefficients contain polynomial delay terms are proved by exploiting the Banach fixed point theorem. Then thepropagation of chaos between interacting particle system and non-interacting system in Lp sense is shown. We find that even if the delay term satisfies the polynomial growth condition, the unmodified classical EM scheme still can approximate the corresponding interacting particle system without the particle corruption. The convergence rates are revealed for H ∈ (0, 1/2) ∪ (1/2, 1). Finally, as an example that closely fits the original equation, a stochastic opinion dynamics model with both extrinsic memory and intrinsic memory is simulated to illustrate the plausibility of the theoretical result.
published_date	2025-10-01T05:28:22Z
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score	11.089386

Euler–Maruyama scheme for delay-type stochastic McKean-Vlasov equations driven by fractional Brownian motion

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