Ergodic properties of anomalous diffusion processes

Journal Article · Thu Sep 15 00:00:00 EDT 2011 · Annals of Physics (New York)

DOI:https://doi.org/10.1016/j.aop.2011.04.015· OSTI ID:21583333

Magdziarz, Marcin; Weron, Aleksander

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.

• OSTI ID: 21583333
• Journal Information: Annals of Physics (New York), Vol. 326, 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.; ISSN 0003-4916
• Country of Publication: United States
• Language: English

Related Subjects

71 CLASSICAL AND QUANTUM MECHANICS
GENERAL PHYSICS
ASYMPTOTIC SOLUTIONS
CORRELATIONS
DIFFUSION
FOKKER-PLANCK EQUATION
STOCHASTIC PROCESSES
DIFFERENTIAL EQUATIONS
EQUATIONS
MATHEMATICAL SOLUTIONS
PARTIAL DIFFERENTIAL EQUATIONS