Ergodic properties of anomalous diffusion processes

In this paper we study ergodic properties of some classes of anomalous diffusion processes. Using the recently developed measure of dependence called the Correlation Cascade, we derive a generalization of the classical Khinchin theorem. This result allows us to determine ergodic properties of Lévy-driven stochastic processes. Moreover, we analyze the asymptotic behavior of two different fractional Ornstein–Uhlenbeck processes, both originating from subdiffusive dynamics. We show that only one of them is ergodic.

► We derive a generalization of the classical Khinchin ergodic theorem for the general class of Levy-driven processes.
► We study ergodic properties of stable and tempered stable processes.
► We verify ergodicity and mixing of two fractional Ornstein–Uhlenbeck processes, both originating from subdiffusive dynamics.