Empirical approximation to invariant measures of non-degenerate McKean-Vlasov dynamics

2023/10/30 by Wenjing Cao, Kai Du, Cao, Wenjing +1
Economics, Econometrics and Finance · Physics and Astronomy · #37M25 #60B10 #60F25 #60H10 #Complex Systems and Time Series Analysis #FOS: Mathematics #Probability (math.PR) #Statistical Mechanics and Entropy #Theoretical and Computational Physics

paper · pdf · doi:10.48550/arxiv.2310.19302

openalex publication_date 2023/10/30 · openalex created_date 2023/11/01 · openalex updated_date 2026/07/28

Abstract

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.

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