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Title: Ergodic properties of anomalous diffusion processes

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 Levy-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. - Highlights: > 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.

Authors:
;
Publication Date:
OSTI Identifier:
21583333
Resource Type:
Journal Article
Journal Name:
Annals of Physics (New York)
Additional Journal Information:
Journal Volume: 326; Journal Issue: 9; Other Information: DOI: 10.1016/j.aop.2011.04.015; PII: S0003-4916(11)00081-9; Copyright (c) 2011 Elsevier Science B.V., Amsterdam, The Netherlands, All rights reserved.; Journal ID: ISSN 0003-4916
Country of Publication:
United States
Language:
English
Subject:
71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSICS; ASYMPTOTIC SOLUTIONS; CORRELATIONS; DIFFUSION; FOKKER-PLANCK EQUATION; STOCHASTIC PROCESSES; DIFFERENTIAL EQUATIONS; EQUATIONS; MATHEMATICAL SOLUTIONS; PARTIAL DIFFERENTIAL EQUATIONS

Citation Formats

Magdziarz, Marcin, E-mail: marcin.magdziarz@pwr.wroc.pl, and Weron, Aleksander. Ergodic properties of anomalous diffusion processes. United States: N. p., 2011. Web. doi:10.1016/j.aop.2011.04.015.
Magdziarz, Marcin, E-mail: marcin.magdziarz@pwr.wroc.pl, & Weron, Aleksander. Ergodic properties of anomalous diffusion processes. United States. doi:10.1016/j.aop.2011.04.015.
Magdziarz, Marcin, E-mail: marcin.magdziarz@pwr.wroc.pl, and Weron, Aleksander. Thu . "Ergodic properties of anomalous diffusion processes". United States. doi:10.1016/j.aop.2011.04.015.
@article{osti_21583333,
title = {Ergodic properties of anomalous diffusion processes},
author = {Magdziarz, Marcin, E-mail: marcin.magdziarz@pwr.wroc.pl and Weron, Aleksander},
abstractNote = {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 Levy-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. - Highlights: > 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.},
doi = {10.1016/j.aop.2011.04.015},
journal = {Annals of Physics (New York)},
issn = {0003-4916},
number = 9,
volume = 326,
place = {United States},
year = {2011},
month = {9}
}