Classification of random trajectories based on the fractional Levy stable motion

In this paper we propose a new approach for the analysis of experimental data based on the fractional Levy stable motion (FLSM) and apply it to the Golding-Cox mRNA dataset. The FLSM takes into account non-Gaussian alpha-stable distributions and is characterized by the memory parameter d =H 1/alpha, where H is the Hurst exponent. The sign of d indicates the type of diffusion: d = 0 for Levy diffusion, d < 0 for subdiffusion and d > 0 for superdiffusion. By estimating the memory parameter for trajectories, we obtain their classification along the x and y coordinates independently. It appears that most of the trajectories are subdiffusive, other follow the Levy-diffusion, but none of them is superdiffusive. We also justify presence of the non-Gaussian alpha-stable distribution by five different goodness-of-fit tests. We note that the classification procedure presented here can be applied to other experimental data which exhibit a non-Gaussian behavior. (C) 2021 The Author(s). Published by Elsevier Ltd.