Random coefficient autoregressive processes describe Brownian yet non-Gaussian diffusion in heterogeneous systems
- Many studies on biological and soft matter systems report the joint presence of a linear mean-squared displacement and a non-Gaussian probability density exhibiting, for instance, exponential or stretched-Gaussian tails. This phenomenon is ascribed to the heterogeneity of the medium and is captured by random parameter models such as ‘superstatistics’ or ‘diffusing diffusivity’. Independently, scientists working in the area of time series analysis and statistics have studied a class of discrete-time processes with similar properties, namely, random coefficient autoregressive models. In this work we try to reconcile these two approaches and thus provide a bridge between physical stochastic processes and autoregressive models.Westart from the basic Langevin equation of motion with time-varying damping or diffusion coefficients and establish the link to random coefficient autoregressive processes. By exploring that link we gain access to efficient statistical methods which can help to identify data exhibiting Brownian yet non-GaussianMany studies on biological and soft matter systems report the joint presence of a linear mean-squared displacement and a non-Gaussian probability density exhibiting, for instance, exponential or stretched-Gaussian tails. This phenomenon is ascribed to the heterogeneity of the medium and is captured by random parameter models such as ‘superstatistics’ or ‘diffusing diffusivity’. Independently, scientists working in the area of time series analysis and statistics have studied a class of discrete-time processes with similar properties, namely, random coefficient autoregressive models. In this work we try to reconcile these two approaches and thus provide a bridge between physical stochastic processes and autoregressive models.Westart from the basic Langevin equation of motion with time-varying damping or diffusion coefficients and establish the link to random coefficient autoregressive processes. By exploring that link we gain access to efficient statistical methods which can help to identify data exhibiting Brownian yet non-Gaussian diffusion.…
Author details: | Jakub ŚlęzakORCiD, Krzysztof BurneckiORCiD, Ralf MetzlerORCiDGND |
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DOI: | https://doi.org/10.1088/1367-2630/ab3366 |
ISSN: | 1367-2630 |
Title of parent work (English): | New Journal of Physics |
Publisher: | Deutsche Physikalische Gesellschaft ; IOP, Institute of Physics |
Place of publishing: | Bad Honnef und London |
Publication type: | Article |
Language: | English |
Date of first publication: | 2019/07/30 |
Publication year: | 2019 |
Release date: | 2019/11/12 |
Tag: | Brownian yet non-Gaussian diffusion; Langevin equation; autoregressive models; codifference; diffusing diffusivity; diffusion; superstatistics; time series analysis |
Volume: | 21 |
Number of pages: | 18 |
Funding institution: | Universität Potsdam |
Funding number: | PA 2019_78 |
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 |
License (German): | Creative Commons - Namensnennung, 3.0 Deutschland |
External remark: | Zweitveröffentlichung in der Schriftenreihe Postprints der Universität Potsdam : Mathematisch-Naturwissenschaftliche Reihe ; 765 |