A Weak Overdamped Limit Theorem for Langevin Processes - Archive ouverte HAL Access content directly
Journal Articles ALEA : Latin American Journal of Probability and Mathematical Statistics Year : 2020

A Weak Overdamped Limit Theorem for Langevin Processes

Abstract

In this paper, we prove convergence in distribution of Langevin processes in the overdamped asymptotics. The proof relies on the classical perturbed test function (or corrector) method, which is used both to show tightness in path space, and to identify the extracted limit with a martingale problem. The result holds assuming the continuity of the gradient of the potential energy, and a mild control of the initial kinetic energy.
Fichier principal
Vignette du fichier
weak_limit_theorem.pdf (267.28 Ko) Télécharger le fichier
Origin : Files produced by the author(s)
Loading...

Dates and versions

hal-01596954 , version 1 (28-09-2017)
hal-01596954 , version 2 (08-03-2019)

Identifiers

Cite

Mathias Rousset, Yushun Xu, Pierre-André Zitt. A Weak Overdamped Limit Theorem for Langevin Processes. ALEA : Latin American Journal of Probability and Mathematical Statistics, 2020, 17 (1), pp.1-21. ⟨10.30757/ALEA.v17-01⟩. ⟨hal-01596954v2⟩
361 View
654 Download

Altmetric

Share

Gmail Facebook X LinkedIn More