Overdamped limit at stationarity for non-equilibrium Langevin diffusions

2021/10/04 by Monmarché, Pierre, Ramil, Mouad · 1 citation
#FOS: Mathematics #Probability (math.PR)

paper · doi:10.48550/arxiv.2110.01238

Abstract

In this note, we establish that the stationary distribution of a possibly non-equilibrium Langevin diffusion converges, as the damping parameter goes to infinity (or equivalently in the Smoluchowski-Kramers vanishing mass limit), toward a tensor product of the stationary distribution of the corresponding overdamped process and of a Gaussian distribution.

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• Exponential Ergodicity in Relative Entropy and L²-Wasserstein Distance for non-equilibrium partially dissipative Kinetic SDEs

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