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.
CITATION STYLE
Leimkuhler, B., & Sachs, M. (2019). Ergodic Properties of Quasi-Markovian Generalized Langevin Equations with Configuration Dependent Noise and Non-conservative Force. In Springer Proceedings in Mathematics and Statistics (Vol. 282, pp. 282–330). Springer New York LLC. https://doi.org/10.1007/978-3-030-15096-9_8
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