A flexible split‐step scheme for solving McKean‐Vlasov stochastic differential equations

Detalhes bibliográficos
Autor(a) principal: Chen, Xingyuan
Data de Publicação: 2022
Outros Autores: dos Reis, Gonçalo
Tipo de documento: Artigo
Idioma: eng
Título da fonte: Repositório Científico de Acesso Aberto de Portugal (Repositórios Cientìficos)
Texto Completo: http://hdl.handle.net/10362/151081
Resumo: Funding Information: The authors would like to thank the 3 referees for their thorough work and suggestions that led to non trivial improvements. Publisher Copyright: © 2022 The Authors
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spelling A flexible split‐step scheme for solving McKean‐Vlasov stochastic differential equationsA flexible split‐step scheme for MV‐SDEsInteracting particle systemsMcKean-Vlasov equationsSplit-step methodsSuperlinear growthComputational MathematicsApplied MathematicsFunding Information: The authors would like to thank the 3 referees for their thorough work and suggestions that led to non trivial improvements. Publisher Copyright: © 2022 The AuthorsWe present an implicit Split-Step explicit Euler type Method (dubbed SSM) for the simulation of McKean-Vlasov Stochastic Differential Equations (MV-SDEs) with drifts of superlinear growth in space, Lipschitz in measure and non-constant Lipschitz diffusion coefficient. The scheme is designed to leverage the structure induced by the interacting particle approximation system, including parallel implementation and the solvability of the implicit equation. The scheme attains the classical 1/2 root mean square error (rMSE) convergence rate in stepsize and closes the gap left by [1] regarding efficient implicit methods and their convergence rate for this class of McKean-Vlasov SDEs. A sufficient condition for mean-square contractivity of the scheme is presented. Several numerical examples are presented, including a comparative analysis to other known algorithms for this class (Taming and Adaptive time-stepping) across parallel and non-parallel implementations.CMA - Centro de Matemática e AplicaçõesRUNChen, Xingyuandos Reis, Gonçalo2023-03-22T22:29:10Z2022-08-152022-08-15T00:00:00Zinfo:eu-repo/semantics/publishedVersioninfo:eu-repo/semantics/articleapplication/pdfhttp://hdl.handle.net/10362/151081engChen, X., & dos Reis, G. (2022). A flexible split‐step scheme for solving McKean‐Vlasov stochastic differential equations: A flexible split‐step scheme for MV‐SDEs. Applied Mathematics and Computation, 427, [127180]. https://doi.org/10.1016/j.amc.2022.1271800096-3003PURE: 56628952https://doi.org/10.1016/j.amc.2022.127180info:eu-repo/semantics/openAccessreponame:Repositório Científico de Acesso Aberto de Portugal (Repositórios Cientìficos)instname:Agência para a Sociedade do Conhecimento (UMIC) - FCT - Sociedade da Informaçãoinstacron:RCAAP2024-03-11T05:33:32Zoai:run.unl.pt:10362/151081Portal AgregadorONGhttps://www.rcaap.pt/oai/openaireopendoar:71602024-03-20T03:54:27.234676Repositório Científico de Acesso Aberto de Portugal (Repositórios Cientìficos) - Agência para a Sociedade do Conhecimento (UMIC) - FCT - Sociedade da Informaçãofalse
dc.title.none.fl_str_mv A flexible split‐step scheme for solving McKean‐Vlasov stochastic differential equations
A flexible split‐step scheme for MV‐SDEs
title A flexible split‐step scheme for solving McKean‐Vlasov stochastic differential equations
spellingShingle A flexible split‐step scheme for solving McKean‐Vlasov stochastic differential equations
Chen, Xingyuan
Interacting particle systems
McKean-Vlasov equations
Split-step methods
Superlinear growth
Computational Mathematics
Applied Mathematics
title_short A flexible split‐step scheme for solving McKean‐Vlasov stochastic differential equations
title_full A flexible split‐step scheme for solving McKean‐Vlasov stochastic differential equations
title_fullStr A flexible split‐step scheme for solving McKean‐Vlasov stochastic differential equations
title_full_unstemmed A flexible split‐step scheme for solving McKean‐Vlasov stochastic differential equations
title_sort A flexible split‐step scheme for solving McKean‐Vlasov stochastic differential equations
author Chen, Xingyuan
author_facet Chen, Xingyuan
dos Reis, Gonçalo
author_role author
author2 dos Reis, Gonçalo
author2_role author
dc.contributor.none.fl_str_mv CMA - Centro de Matemática e Aplicações
RUN
dc.contributor.author.fl_str_mv Chen, Xingyuan
dos Reis, Gonçalo
dc.subject.por.fl_str_mv Interacting particle systems
McKean-Vlasov equations
Split-step methods
Superlinear growth
Computational Mathematics
Applied Mathematics
topic Interacting particle systems
McKean-Vlasov equations
Split-step methods
Superlinear growth
Computational Mathematics
Applied Mathematics
description Funding Information: The authors would like to thank the 3 referees for their thorough work and suggestions that led to non trivial improvements. Publisher Copyright: © 2022 The Authors
publishDate 2022
dc.date.none.fl_str_mv 2022-08-15
2022-08-15T00:00:00Z
2023-03-22T22:29:10Z
dc.type.status.fl_str_mv info:eu-repo/semantics/publishedVersion
dc.type.driver.fl_str_mv info:eu-repo/semantics/article
format article
status_str publishedVersion
dc.identifier.uri.fl_str_mv http://hdl.handle.net/10362/151081
url http://hdl.handle.net/10362/151081
dc.language.iso.fl_str_mv eng
language eng
dc.relation.none.fl_str_mv Chen, X., & dos Reis, G. (2022). A flexible split‐step scheme for solving McKean‐Vlasov stochastic differential equations: A flexible split‐step scheme for MV‐SDEs. Applied Mathematics and Computation, 427, [127180]. https://doi.org/10.1016/j.amc.2022.127180
0096-3003
PURE: 56628952
https://doi.org/10.1016/j.amc.2022.127180
dc.rights.driver.fl_str_mv info:eu-repo/semantics/openAccess
eu_rights_str_mv openAccess
dc.format.none.fl_str_mv application/pdf
dc.source.none.fl_str_mv reponame:Repositório Científico de Acesso Aberto de Portugal (Repositórios Cientìficos)
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instacron:RCAAP
instname_str Agência para a Sociedade do Conhecimento (UMIC) - FCT - Sociedade da Informação
instacron_str RCAAP
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reponame_str Repositório Científico de Acesso Aberto de Portugal (Repositórios Cientìficos)
collection Repositório Científico de Acesso Aberto de Portugal (Repositórios Cientìficos)
repository.name.fl_str_mv Repositório Científico de Acesso Aberto de Portugal (Repositórios Cientìficos) - Agência para a Sociedade do Conhecimento (UMIC) - FCT - Sociedade da Informação
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