Spurious ergodicity breaking in normal and fractional Ornstein–Uhlenbeck process
- The Ornstein–Uhlenbeck process is a stationary and ergodic Gaussian process, that is fully determined by its covariance function and mean. We show here that the generic definitions of the ensemble- and time-averaged mean squared displacements fail to capture these properties consistently, leading to a spurious ergodicity breaking. We propose to remedy this failure by redefining the mean squared displacements such that they reflect unambiguously the statistical properties of any stochastic process. In particular we study the effect of the initial condition in the Ornstein–Uhlenbeck process and its fractional extension. For the fractional Ornstein–Uhlenbeck process representing typical experimental situations in crowded environments such as living biological cells, we show that the stationarity of the process delicately depends on the initial condition.
Author details: | Yousof MardoukhiORCiDGND, Aleksei ChechkinORCiDGND, Ralf MetzlerORCiDGND |
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DOI: | https://doi.org/10.1088/1367-2630/ab950b |
ISSN: | 1367-2630 |
Title of parent work (English): | New Journal of Physics |
Publisher: | IOP |
Place of publishing: | London |
Publication type: | Article |
Language: | English |
Date of first publication: | 2020/01/10 |
Publication year: | 2020 |
Release date: | 2020/08/27 |
Tag: | Ornstein–Uhlenbeck process; ensemble and time averaged mean squared displacement; stationary stochastic process |
Volume: | 22 |
Number of pages: | 18 |
Funding institution: | Universität Potsdam |
Funding number: | PA 2020_061 |
Organizational units: | Mathematisch-Naturwissenschaftliche Fakultät / Institut für Physik und Astronomie |
DDC classification: | 5 Naturwissenschaften und Mathematik / 53 Physik / 530 Physik |
Peer review: | Referiert |
Grantor: | Publikationsfonds der Universität Potsdam |
Publishing method: | Open Access / Gold Open-Access |
License (German): | CC-BY - Namensnennung 4.0 International |
External remark: | Zweitveröffentlichung in der Schriftenreihe Postprints der Universität Potsdam : Mathematisch-Naturwissenschaftliche Reihe ; 981 |
External remark: | This article is part of this cumulative dissertation |