Mosco convergence of independent particles and applications to particle systems with self-duality
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arXiv
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| Format: | Preprint |
| Veröffentlicht: |
2024
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| _version_ | 1866929401944342528 |
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| author | Ayala, Mario |
| author_facet | Ayala, Mario |
| contents | We consider a sequence of Markov processes $\lbrace X_t^n \mid n \in \mathbb{N} \rbrace$ with Dirichlet forms converging in the Mosco sense of Kuwae and Shioya to the Dirichlet form associated with a Markov process $X_t$. Under this assumption, we demonstrate that for any natural number $k$, the sequence of Dirichlet forms corresponding to the Markov processes generated by $k$ independent copies of $\lbrace X_t^n \mid n \in \mathbb{N} \rbrace$ also converges. As expected, the limit of this convergence is the Dirichlet form associated with $k$ independent copies of the process $X_t$. We provide applications of this result in the context of interacting particle systems with Markov moment duality. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2406_19088 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Mosco convergence of independent particles and applications to particle systems with self-duality Ayala, Mario Probability We consider a sequence of Markov processes $\lbrace X_t^n \mid n \in \mathbb{N} \rbrace$ with Dirichlet forms converging in the Mosco sense of Kuwae and Shioya to the Dirichlet form associated with a Markov process $X_t$. Under this assumption, we demonstrate that for any natural number $k$, the sequence of Dirichlet forms corresponding to the Markov processes generated by $k$ independent copies of $\lbrace X_t^n \mid n \in \mathbb{N} \rbrace$ also converges. As expected, the limit of this convergence is the Dirichlet form associated with $k$ independent copies of the process $X_t$. We provide applications of this result in the context of interacting particle systems with Markov moment duality. |
| title | Mosco convergence of independent particles and applications to particle systems with self-duality |
| topic | Probability |
| url | https://arxiv.org/abs/2406.19088 |