Ergodic properties of quasi-Markovian generalized Langevin equations with configuration dependent noise and non-conservative force

2018/04/11 by Leimkuhler, Benedict, Sachs, Matthias
#FOS: Mathematics #Probability (math.PR)

paper · doi:10.48550/arxiv.1804.04029

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.

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