Empirical approximation to invariant measures of non-degenerate McKean-Vlasov dynamics
Fuente:
arXiv
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| Autori principali: | , |
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| Natura: | Preprint |
| Pubblicazione: |
2023
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| _version_ | 1866910305645232128 |
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| author | Cao, Wenjing Du, Kai |
| author_facet | Cao, Wenjing Du, Kai |
| contents | This paper studies the approximation of invariant measures of McKean-Vlasov dynamics with non-degenerate additive noise. While prior findings necessitated a strong monotonicity condition on the McKean-Vlasov process, we expand these results to encompass dissipative and weak interaction scenarios. Utilizing a reflection coupling technique, we prove that the empirical measures of the McKean-Vlasov process and its path-dependent counterpart can converge to the invariant measure in the Wasserstein metric. The Curie-Weiss mean-field lattice model serves as a numerical example to illustrate empirical approximation. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2310_19302 |
| institution | arXiv |
| publishDate | 2023 |
| record_format | arxiv |
| spellingShingle | Empirical approximation to invariant measures of non-degenerate McKean-Vlasov dynamics Cao, Wenjing Du, Kai Probability 60B10, 37M25, 60F25, 60H10 This paper studies the approximation of invariant measures of McKean-Vlasov dynamics with non-degenerate additive noise. While prior findings necessitated a strong monotonicity condition on the McKean-Vlasov process, we expand these results to encompass dissipative and weak interaction scenarios. Utilizing a reflection coupling technique, we prove that the empirical measures of the McKean-Vlasov process and its path-dependent counterpart can converge to the invariant measure in the Wasserstein metric. The Curie-Weiss mean-field lattice model serves as a numerical example to illustrate empirical approximation. |
| title | Empirical approximation to invariant measures of non-degenerate McKean-Vlasov dynamics |
| topic | Probability 60B10, 37M25, 60F25, 60H10 |
| url | https://arxiv.org/abs/2310.19302 |