The Euler-Maruyama method for invariant measures of McKean-Vlasov stochastic differential equations
Probability
2026-04-17 v1
Abstract
This paper investigates the approximation of invariant measures for McKean-Vlasov stochastic differential equations (SDEs) using the Euler-Maruyama (EM) scheme under a monotonicity condition. Firstly, the convergence of the numerical solution from the EM scheme to its continuous-time counterpart is established. Secondly, we show that the numerical solution admits a unique invariant measure and derive its convergence rate under the Wasserstein metric. In parallel, it is demonstrated that the associated particle system also possesses these properties.
Keywords
Cite
@article{arxiv.2604.14543,
title = {The Euler-Maruyama method for invariant measures of McKean-Vlasov stochastic differential equations},
author = {Zhen Wang and Mingyan Wu},
journal= {arXiv preprint arXiv:2604.14543},
year = {2026}
}