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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| Tipo de recurso: | artículo |
| Estado: | Versión publicada |
| Fecha de publicación: | 2023 |
| País: | España |
| Institución: | Universidad de Barcelona |
| Repositorio: | Dipòsit Digital de la UB |
| OAI Identifier: | oai:diposit.ub.edu:2445/217593 |
| Acceso en línea: | https://hdl.handle.net/2445/217593 |
| Access Level: | acceso abierto |
| Palabra clave: | Operadors diferencials Teoremes de límit (Teoria de probabilitats) Convergència (Matemàtica) Processos de Markov Differential operators Limit theorems (Probability theory) Convergence Markov processes |
| Sumario: | 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. |
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