Weak approximation of kinetic SDEs: closing the criticality gap

TL;DR

This paper proves that a tamed Euler-Maruyama scheme for kinetic SDEs with integrable drifts converges in density at rate 1/2, regardless of the criticality gap, advancing understanding of numerical methods for such equations.

Contribution

It establishes the convergence rate of the scheme independently of the criticality gap, filling a gap in the analysis of kinetic SDE approximations.

Findings

Convergence rate of 1/2 for the scheme's density

Independence from the criticality gap

Extension to kinetic SDEs with integrable drifts

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.