Random coefficient autoregressive processes describe Brownian yet non-Gaussian diffusion in heterogeneous systems

Abstract

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.

28 pages, 9 figures, IOP LaTeX

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Cited by in corpus (10)

• The Hitchhiker model for Laplace diffusion processes in the cell environment
• Brownian motion and beyond: first-passage, power spectrum, non-Gaussianity, and anomalous diffusion
• On relation between generalized diffusion equations and subordination schemes
• Universal spectral features of different classes of random diffusivity processes
• Leveraging large-deviation statistics to decipher the stochastic properties of measured trajectories
• Non-Gaussian displacement distributions in models of heterogeneous active particle dynamics
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• Superstatistical approach of the anomalous exponent for scaled Brownian motion
• Anomalous Diffusion: Fractional Brownian Motion vs. Fractional Ito Motion
• Changepoint detection in random coefficient autoregressive models