  In many physical or biological systems, diffusion can be described by
Brownian motions with stochastic diffusion coefficients (DCs). In the present
study, we investigate properties of the diffusion with a broad class of
stochastic DCs with a novel approach. We show that for a finite time, the
propagator is non-Gaussian and heavy-tailed. This means that when the mean
square displacements are the same, for a finite time, some of the diffusing
particles with stochastic DCs diffuse farther than the particles with
deterministic DCs or exhibiting a fractional Brownian motion. We also show that
when a stochastic DC is ergodic, the propagator converges to a Gaussian
distribution in the long time limit. The speed of convergence is determined by
the autocovariance function of the DC.
