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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 Orcid Logo

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

Swansea University Author: Chenggui Yuan Orcid Logo

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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
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URI: https://cronfa.swan.ac.uk/Record/cronfa69505
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 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.
Keywords: Delay-type stochastic mcKean-vlasov equations; Fractional brownian motion; Propagation of chaos; Euler–maruyama scheme; Strong convergence rate
College: Faculty of Science and Engineering
Funders: 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).
Start Page: 108927

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