Couplings and quantitative contraction rates for Langevin dynamics

摘要: We introduce a new probabilistic approach to quantify convergence equilibrium for (kinetic) Langevin processes. In contrast previous analytic approaches that focus on the associated kinetic Fokker-Planck equation, our is based specific combination of reflection and synchronous coupling two solutions equation. It yields contractions in particular Wasserstein distance, it provides rather precise bounds at borderline between overdamped underdamped regime. particular, we are able recover behavior terms explicit lower contraction rate. For example, rescaled double-well potential with local minima distance a, obtain bound rate order Ω(a−1) provided friction coefficient Θ(a−1)