Markov chain approximations for nonsymmetric processes

The aim of this article is to prove that diffusion processes in $\mathbb{R}^d$ with a drift can be approximated by suitable Markov chains on $n^{-1} \mathbb{Z}^d$. Moreover, we investigate sufficient conditions on the edge weights which guarantee convergence of the associated Markov chains to such M...

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Detalhes bibliográficos
Autor: Weidner, Marvin
Formato: artículo
Estado:Versión publicada
Fecha de publicación:2023
País:España
Recursos:Universidad de Barcelona
Repositorio:Dipòsit Digital de la UB
OAI Identifier:oai:diposit.ub.edu:2445/217593
Acesso em linha:https://hdl.handle.net/2445/217593
Access Level:acceso abierto
Palavra-chave:Operadors diferencials
Teoremes de límit (Teoria de probabilitats)
Convergència (Matemàtica)
Processos de Markov
Differential operators
Limit theorems (Probability theory)
Convergence
Markov processes
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oai_identifier_str oai:diposit.ub.edu:2445/217593
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repository_id_str
spelling Markov chain approximations for nonsymmetric processesWeidner, MarvinOperadors diferencialsTeoremes de límit (Teoria de probabilitats)Convergència (Matemàtica)Processos de MarkovDifferential operatorsLimit theorems (Probability theory)ConvergenceMarkov processesThe aim of this article is to prove that diffusion processes in $\mathbb{R}^d$ with a drift can be approximated by suitable Markov chains on $n^{-1} \mathbb{Z}^d$. Moreover, we investigate sufficient conditions on the edge weights which guarantee convergence of the associated Markov chains to such Markov processes. Analogous questions are answered for a large class of nonsymmetric jump processes. The proofs of our results rely on regularity estimates for weak solutions to the corresponding nonsymmetric parabolic equations and Dirichlet form techniques.Elsevier B.V.2023info:eu-repo/semantics/articleinfo:eu-repo/semantics/publishedVersionapplication/pdfhttps://hdl.handle.net/2445/217593Articles publicats en revistes (Matemàtiques i Informàtica)reponame:Dipòsit Digital de la UBinstname:Universidad de BarcelonaInglésReproducció del document publicat a: https://doi.org/10.1016/j.spa.2023.01.009Stochastic Processes and their Applications, 2023, vol. 158, p. 238-281https://doi.org/10.1016/j.spa.2023.01.009cc-by (c) Marvin Weidner., 2023http://creativecommons.org/licenses/by/3.0/es/info:eu-repo/semantics/openAccessoai:diposit.ub.edu:2445/2175932026-05-27T06:46:51Z
dc.title.none.fl_str_mv Markov chain approximations for nonsymmetric processes
title Markov chain approximations for nonsymmetric processes
spellingShingle Markov chain approximations for nonsymmetric processes
Weidner, Marvin
Operadors diferencials
Teoremes de límit (Teoria de probabilitats)
Convergència (Matemàtica)
Processos de Markov
Differential operators
Limit theorems (Probability theory)
Convergence
Markov processes
title_short Markov chain approximations for nonsymmetric processes
title_full Markov chain approximations for nonsymmetric processes
title_fullStr Markov chain approximations for nonsymmetric processes
title_full_unstemmed Markov chain approximations for nonsymmetric processes
title_sort Markov chain approximations for nonsymmetric processes
dc.creator.none.fl_str_mv Weidner, Marvin
author Weidner, Marvin
author_facet Weidner, Marvin
author_role author
dc.subject.none.fl_str_mv Operadors diferencials
Teoremes de límit (Teoria de probabilitats)
Convergència (Matemàtica)
Processos de Markov
Differential operators
Limit theorems (Probability theory)
Convergence
Markov processes
topic Operadors diferencials
Teoremes de límit (Teoria de probabilitats)
Convergència (Matemàtica)
Processos de Markov
Differential operators
Limit theorems (Probability theory)
Convergence
Markov processes
description The aim of this article is to prove that diffusion processes in $\mathbb{R}^d$ with a drift can be approximated by suitable Markov chains on $n^{-1} \mathbb{Z}^d$. Moreover, we investigate sufficient conditions on the edge weights which guarantee convergence of the associated Markov chains to such Markov processes. Analogous questions are answered for a large class of nonsymmetric jump processes. The proofs of our results rely on regularity estimates for weak solutions to the corresponding nonsymmetric parabolic equations and Dirichlet form techniques.
publishDate 2023
dc.date.none.fl_str_mv 2023
dc.type.none.fl_str_mv info:eu-repo/semantics/article
info:eu-repo/semantics/publishedVersion
format article
status_str publishedVersion
dc.identifier.none.fl_str_mv https://hdl.handle.net/2445/217593
url https://hdl.handle.net/2445/217593
dc.language.none.fl_str_mv Inglés
language_invalid_str_mv Inglés
dc.relation.none.fl_str_mv Reproducció del document publicat a: https://doi.org/10.1016/j.spa.2023.01.009
Stochastic Processes and their Applications, 2023, vol. 158, p. 238-281
https://doi.org/10.1016/j.spa.2023.01.009
dc.rights.none.fl_str_mv cc-by (c) Marvin Weidner., 2023
http://creativecommons.org/licenses/by/3.0/es/
info:eu-repo/semantics/openAccess
rights_invalid_str_mv cc-by (c) Marvin Weidner., 2023
http://creativecommons.org/licenses/by/3.0/es/
eu_rights_str_mv openAccess
dc.format.none.fl_str_mv application/pdf
dc.publisher.none.fl_str_mv Elsevier B.V.
publisher.none.fl_str_mv Elsevier B.V.
dc.source.none.fl_str_mv Articles publicats en revistes (Matemàtiques i Informàtica)
reponame:Dipòsit Digital de la UB
instname:Universidad de Barcelona
instname_str Universidad de Barcelona
reponame_str Dipòsit Digital de la UB
collection Dipòsit Digital de la UB
repository.name.fl_str_mv
repository.mail.fl_str_mv
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score 15,811543

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