Empirical approximation to invariant measures of mean-field Langevin dynamics

Wenjing Cao; Kai Du

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arXiv · 2404.18164

Empirical approximation to invariant measures of mean-field Langevin dynamics

Wenjing Cao·Kai Du

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Abstract

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.

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Wenjing Cao, Kai Du. 2024-04-28. Empirical approximation to invariant measures of mean-field Langevin dynamics. https://arxiv.org/abs/2404.18164

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