Section: New Results

Error Analysis of Modified Langevin Dynamics

Participants : Zofia Trstanova, Gabriel Stoltz, Stephane Redon.

We performed a mathematical analysis of modified Langevin dynamics. The aim of this work was first to prove the ergodicity of the modified Langevin dynamics (which fails to be hypoelliptic), and next to analyze how the asymptotic variance on ergodic averages depends on the parameters of the modified kinetic energy. Numerical results illustrated the approach, both for low-dimensional systems where we resorted to a Galerkin approximation of the generator, and for more realistic systems using Monte Carlo simulations.