Convergence rate of Euler-Maruyama scheme for McKean-Vlasov SDEs with density-dependent drift

Abstract

In this paper, we study weak well-posedness of a McKean-Vlasov stochastic differential equations (SDEs) whose drift is density-dependent and whose diffusion is constant. The existence part is due to Hölder stability estimates of the associated Euler-Maruyama scheme. The uniqueness part is due to that of the associated Fokker-Planck equation. We also obtain convergence rate in weighted L1 norm for the Euler-Maruyama scheme.

Keywords

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Anh-Dung Le, and Stéphane Villeneuve, “Convergence rate of Euler-Maruyama scheme for McKean-Vlasov SDEs with density-dependent drift”, Stochastics and Dynamics, 2026, forthcoming.

Reference

Anh-Dung Le, and Stéphane Villeneuve, “Convergence rate of Euler-Maruyama scheme for McKean-Vlasov SDEs with density-dependent drift”, TSE Working Paper, n. 26-1768, May 2026.