Characterising stochastic motion in heterogeneous media driven by coloured non-Gaussian noise

We study the stochastic motion of a test particle in a heterogeneous medium in terms of a position dependent diffusion coefficient mimicking measured deterministic diffusivity gradients in biological cells or the inherent heterogeneity of geophysical systems. Compared to previous studies we here investigate the effect of the interplay of anomalous diffusion effected by position dependent diffusion coefficients and coloured non-Gaussian noise. The latter is chosen to be distributed according to Tsallis' q-distribution, representing a popular example for a non-extensive statistic. We obtain the ensemble and time averaged mean squared displacements for this generalised process and establish its non-ergodic properties as well as analyse the non-Gaussian nature of the associated displacement distribution. We consider both non-stratified and stratified environments.

Automated summary

In this study, the stochastic motion of a test particle in a heterogeneous medium with a position dependent diffusion coefficient is examined, considering the interplay of anomalous diffusion and colored non-Gaussian noise. The Tsallis' q-distribution is used to represent the non-extensive statistic. The research reveals non-ergodic properties of the process and analyzes the non-Gaussian nature of the displacement distribution.