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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.show moreshow less

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Metadaten
Author:Jakub ŚlęzakORCiD, Krzysztof BurneckiORCiD, Ralf MetzlerORCiDGND
DOI:https://doi.org/10.1088/1367-2630/ab3366
ISSN:1367-2630
Parent Title (English):New Journal of Physics
Publisher:Deutsche Physikalische Gesellschaft ; IOP, Institute of Physics
Place of publication:Bad Honnef und London
Document Type:Article
Language:English
Date of first Publication:2019/07/30
Year of Completion: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
Pagenumber:18
Funder:Universität Potsdam
Grant Number:PA 2019_78
Organizational units:Mathematisch-Naturwissenschaftliche Fakultät / Institut für Physik und Astronomie
Dewey Decimal Classification:5 Naturwissenschaften und Mathematik / 53 Physik / 530 Physik
Peer Review:Referiert
Grantor:Publikationsfonds der Universität Potsdam
Publication Way:Open Access
Licence (German):License LogoCreative Commons - Namensnennung, 3.0 Deutschland
Notes extern:Zweitveröffentlichung in der Schriftenreihe Postprints der Universität Potsdam : Mathematisch-Naturwissenschaftliche Reihe ; 765