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Article Dans Une Revue ALEA : Latin American Journal of Probability and Mathematical Statistics Année : 2020

A Weak Overdamped Limit Theorem for Langevin Processes

Résumé

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.
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Dates et versions

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

Identifiants

Citer

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⟩
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