Empirical approximation to invariant measures of mean-field Langevin dynamics

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.