Ergodic Properties of Quasi-Markovian Generalized Langevin Equations with Configuration Dependent Noise and Non-conservative Force

Leimkuhler, Benedict and Sachs, Matthias (2019) Ergodic Properties of Quasi-Markovian Generalized Langevin Equations with Configuration Dependent Noise and Non-conservative Force. In: Stochastic Dynamics Out of Equilibrium - Institut Henri Poincaré, 2017 :. Springer Proceedings in Mathematics & Statistics . Springer Nature, pp. 282-330. ISBN 9783030150952

Abstract

We discuss the ergodic properties of quasi-Markovian stochastic differential equations, providing general conditions that ensure existence and uniqueness of a smooth invariant distribution and exponential convergence of the evolution operator in suitably weighted L∞ spaces, which implies the validity of central limit theorem for the respective solution processes. The main new result is an ergodicity condition for the generalized Langevin equation with configuration-dependent noise and (non-)conservative force.