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arXiv · 2306.13523

Weak error expansion of a stopped numerical scheme for singular Langevin process

Lucas Journel
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Abstract

We show expansion \textit{\`a la Talay-Tubaro} of a stopped numerical scheme 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.

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Lucas Journel. 2023-06-23. Weak error expansion of a stopped numerical scheme for singular Langevin process. https://arxiv.org/abs/2306.13523

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