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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| Format: | article |
| Status: | Published version |
| Publication Date: | 2023 |
| Country: | España |
| Institution: | Varias* (Consorci de Biblioteques Universitáries de Catalunya, Centre de Serveis Científics i Acadèmics de Catalunya) |
| Repository: | Recercat. Dipósit de la Recerca de Catalunya |
| OAI Identifier: | oai:recercat.cat:2445/217593 |
| Online Access: | https://hdl.handle.net/2445/217593 |
| Access Level: | Open access |
| Keyword: | Operadors diferencials Teoremes de límit (Teoria de probabilitats) Convergència (Matemàtica) Processos de Markov Differential operators Limit theorems (Probability theory) Convergence Markov processes |
| Summary: | 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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