Empirical approximation to invariant measures of mean-field Langevin dynamics
Fuente:
arXiv
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| Hauptverfasser: | , |
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| Format: | Preprint |
| Veröffentlicht: |
2024
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| _version_ | 1866913333631778816 |
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| author | Cao, Wenjing Du, Kai |
| author_facet | Cao, Wenjing Du, Kai |
| contents | This paper is concerned with the approximation to invariant measures for Langevin dynamics of McKean--Vlasov type. Under dissipativity and Lipschitz conditions, we prove that the empirical measures of both the mean-field and self-interacting Langevin dynamics converge to the invariant measure in the Wasserstein distance. Numerical experiments are conducted to illustrate theoretical results. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2404_18164 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Empirical approximation to invariant measures of mean-field Langevin dynamics Cao, Wenjing Du, Kai Probability 60B10, 37M25, 82C31, 60H10 This paper is concerned with the approximation to invariant measures for Langevin dynamics of McKean--Vlasov type. Under dissipativity and Lipschitz conditions, we prove that the empirical measures of both the mean-field and self-interacting Langevin dynamics converge to the invariant measure in the Wasserstein distance. Numerical experiments are conducted to illustrate theoretical results. |
| title | Empirical approximation to invariant measures of mean-field Langevin dynamics |
| topic | Probability 60B10, 37M25, 82C31, 60H10 |
| url | https://arxiv.org/abs/2404.18164 |