Session A7 - Stochastic Computation
July 11, 17:30 ~ 17:55 - Room B2
A coupling approach to the kinetic Langevin equation
University of Bonn, Germany - firstname.lastname@example.org
The (kinetic) Langevin equation is an SDE with degenerate noise that describes the motion of a particle in a force field subject to damping and random collisions. It is also closely related to Hamiltonian Monte Carlo methods. An important question is, why in certain cases kinetic Langevin diffusions seem to approach equilibrium faster than overdamped Langevin diffusions.
So far, convergence to equilibrium for kinetic Langevin diffusions has almost exclusively been studied by analytic techniques. In this talk, I present a new probabilistic approach that is based on a specific combination of reflection and synchronuous coupling of two solutions of the Langevin equation. The approach yields rather precise bounds for convergence to equilibrium at the borderline between the overdamped and the underdamped regime, and it may help to shed some light on the open question mentioned above.
Joint work with Arnaud Guillin (Université Blaise Pascal, Clermont-Ferrand, France) and Raphael Zimmer (Universität Bonn, Germany).