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We discuss the ergodic properties of quasi-Markovian stochastic differentialequations, providing general conditions that ensure existence and uniqueness ofa smooth invariant distribution and exponential convergence of the evolutionoperator in suitably weighted $L^{\infty}$ spaces, which implies the validityof central limit theorem for the respective solution processes. The main newresult is an ergodicity condition for the generalized Langevin equation withconfiguration-dependent noise and (non-)conservative force.

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