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

## TL;DR

This paper connects physical models of heterogeneous diffusion with statistical autoregressive models, enabling better analysis of complex diffusion behaviors in biological systems.

## Contribution

It establishes a theoretical link between Langevin equations with variable coefficients and random coefficient autoregressive processes, bridging physics and statistics.

## Key findings

- Provides a framework to identify Brownian yet non-Gaussian diffusion in data.
- Enables application of statistical methods to physical stochastic processes.
- Bridges the gap between physical heterogeneity models and time series analysis.

## 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.