Ergodic properties of anomalous diffusion processes |
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Authors: | Marcin Magdziarz Aleksander Weron |
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Affiliation: | aHugo Steinhaus Center, Institute of Mathematics and Computer Science, Wroclaw University of Technology, Wyspianskiego 27, 50-370 Wroclaw, Poland |
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Abstract: | 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. |
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Keywords: | Ergodicity Mixing Khinchin theorem Anomalous diffusion Ornstein&ndash Uhlenbeck process Fractional Fokker&ndash Planck equation |
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