Section: New Results

Weak overdamped limit theorem for Langevin processes

Participant : Mathias Rousset.

This is a collaboration with Pierre-André Zitt (université Paris Est Marne-la-Vallée).

The Langevin stochastic process is the main model used in molecular dynamics simulation, for instance for the simulation of reactive trajectories of bio-chemical systems with rare event techniques.

In [21], we prove convergence in distribution of Langevin processes in the overdamped diffusion 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.