Weak approximation of kinetic SDEs: closing the criticality gap

Abstract

We study the weak convergence of a generic tamed Euler-Maruyama scheme for kinetic stochastic differential equations (SDEs) with integrable drifts. We show that the marginal density of the considered scheme converges at rate 1/2 to the corresponding marginal density of the SDE. The convergence rate is independent from the criticality gap, which is new compared to previous results.