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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
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 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.
Keywords: The tamed Euler–Maruyama scheme, Neutral multiple-delay stochastic McKean-Vlasov equation, Strong convergence rate, Propagation of chaos
College: Faculty of Science and Engineering
Funders: 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).
Start Page: 115682

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