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.

如今，在扩散率波动的系统中报告非高斯扩散出现的物理系统的数量正在增加。这些系统可能会出现与正常粒子或异常粒子的平均平方位移相关的非高斯扩散。为了包括异常扩散，最近的研究已经研究了按比例缩放的布朗运动（SBM）的超统计量，以描述生物物质中的扩散。在本文中，我们提出了两个随机模型控制的具有随机扩散率的SBM扩散模型。在对随机建模仿真进行全面分析的基础上，我们展示了每种模型的主要显着特征。第一个模型概括了SBM的灰色布朗运动。该模型适用于描述其扩散为非高斯分布的系统。第二个模型推广了最小扩散扩散模型，适用于描述从非高斯过程到标准高斯过程的交叉的系统。这些结果暗示了非高斯扩散过程的丰富类别，它们可能允许正常扩散和异常扩散以及它们之间的交叉。