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 $L^1$ norm for the Euler-Maruyama scheme.