Random diffusivity models for scaled Brownian motion

Abstract

Abstract Nowadays, the number of physical systems that have reported non-Gaussian diffusion emergence in systems whose diffusivity fluctuates is increasing. These systems may present non-Gaussian diffusion associated with a mean square displacement of trace-particles that may be normal or anomalous. To include anomalous diffusion, recent research has investigated superstatistics of scaled Brownian motion (SBM) to describe diffusion in biological matter. In this paper, we propose two diffusion models for SBM with random diffusivity governed by a stochastic equation. Based on a thorough analysis of simulations of stochastic modeling, we have shown the main remarkable features of each model. The first model generalizes the grey Brownian motion for SBM; this model is suitable to describe systems whose diffusion is ever non-Gaussian. The second model generalizes the minimal diffusing diffusivity model and is suitable to describe systems which present crossover from non-Gaussian to standard Gaussian processes. These results imply rich classes of the Non-Gaussian diffusion processes that may admit normal and anomalous diffusion as well as the crossover between them.