The Euler-Maruyama method for invariant measures of McKean-Vlasov stochastic differential equations

Zhen Wang; Mingyan Wu

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arXiv · 2604.14543

The Euler-Maruyama method for invariant measures of McKean-Vlasov stochastic differential equations

Zhen Wang·Mingyan Wu

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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.

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Zhen Wang, Mingyan Wu. 2026-04-16. The Euler-Maruyama method for invariant measures of McKean-Vlasov stochastic differential equations. https://arxiv.org/abs/2604.14543

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