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.

arXiv commentThis paper contains the weak convergence results announced earlier in arXiv:2409.05706. The current preprint is significantly revised to improve clarity. V2: additional details in proofs and updated references