Computing the invariant distribution of McKean-Vlasov SDEs by ergodic simulation

TL;DR

This paper introduces a practical scheme for computing the invariant distribution of ergodic McKean-Vlasov SDEs, providing convergence rates under natural conditions, advancing the numerical analysis of such stochastic systems.

Contribution

The paper presents a new fully implementable ergodic simulation scheme with proven convergence rates for McKean-Vlasov SDEs satisfying a uniform confluence property.

Findings

Established convergence in Wasserstein distance in quadratic mean

Proved almost sure convergence results

Provided explicit rates of convergence under natural conditions

Abstract

We design a fully implementable scheme to compute the invariant distribution of ergodic McKean-Vlasov SDE satisfying a uniform confluence property. Under natural conditions, we prove various convergence results notably we obtain rates for the Wasserstein distance in quadratic mean and almost sure sense.