Article Dans Une Revue Annales de l'Institut Henri Poincaré (B) Probabilités et Statistiques Année : 2025

Uniform minorization condition and convergence bounds for discretizations of kinetic Langevin dynamics

Résumé

We study the convergence in total variation and $V$-norm of discretization schemes of the underdamped Langevin dynamics. Such algorithms are very popular and commonly used in molecular dynamics and computational statistics to approximatively sample from a target distribution of interest. We show first that, for a very large class of schemes, a minorization condition uniform in the stepsize holds. This class encompasses popular methods such as the Euler-Maruyama scheme and the schemes based on splitting strategies. Second, we provide mild conditions ensuring that the class of schemes that we consider satisfies a geometric Foster--Lyapunov drift condition, again uniform in the stepsize. This allows us to derive geometric convergence bounds, with a convergence rate scaling linearly with the stepsize. This kind of result is of prime interest to obtain estimates on norms of solutions to Poisson equations associated with a given numerical method.

Dates et versions

hal-03333501 , version 1 (03-09-2021)

Identifiants

Citer

Alain Durmus, Aurélien Enfroy, Éric Moulines, Gabriel Stoltz. Uniform minorization condition and convergence bounds for discretizations of kinetic Langevin dynamics. Annales de l'Institut Henri Poincaré (B) Probabilités et Statistiques, 2025, 61 (1), ⟨10.1214/23-AIHP1442⟩. ⟨hal-03333501⟩
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