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
Descrição
Resumo: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.