Non-Gaussian transport in tempered fractional Laplace motion

We study a minimal stochastic model for active transport featuring a non-Gaussian displacement probability density function and transient superdiffusion. Our approach is based on a combination of an exponential tempering in the parental fractional Brownian noise correlations, augmented by a gamma-distribution of the diffusivity across the ensemble. For the resulting tempered fractional Laplace motion we derive analytical expressions for the mean-squared displacement, the kurtosis, the non-Gaussianity parameter and the displacement probability density function. We also show via stochastic simulations that the model quantitatively reproduces the main experimental observations in a recent study of active cargo particle transport by a carpet of amoeba cells.