Weak error expansion of a numerical scheme with rejection for singular Langevin process

Abstract

We show expansion à la Talay–Tubaro of a numerical scheme with rejection for the Langevin process in the case of a singular potential. In order to achieve this, we provide estimates on the associated semi-group of the process. The class of admissible potentials includes the Lennard-Jones interaction with confinement, which is an important potential in molecular dynamics and served as the primary motivation for this study.