Journal
NEW JOURNAL OF PHYSICS
Volume 21, Issue -, Pages -Publisher
IOP Publishing Ltd
DOI: 10.1088/1367-2630/ab3366
Keywords
diffusion; Langevin equation; Brownian yet non-Gaussian diffusion; diffusing diffusivity; superstatistics; autoregressive models; time series analysis; codifference
Categories
Funding
- Polish National Science Centre grant [2016/22/M/ST1/00233]
- Beethoven Grant [DFG-NCN 2016/23/G/ST1/04083]
- DFG [ME1535/6-1, ME1535/7-1]
- Alexander von Humboldt Polish Honorary Research Scholarship from the Foundation for Polish Science (Fundacja na rzecz Nauki Polskiej)
- Deutsche Forschungsgemeinschaft (German Research Foundation)
- Open Access Publication Fund of Potsdam University
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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. We start 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.
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