Classification of random trajectories based on the fractional Lévy stable motion

Joanna Janczura, Krzysztof Burnecki, Monika Muszkieta, Aleksander Stanislavsky and Aleksander Weron

Chaos, Solitons & Fractals, 2022, vol. 154, issue C

Abstract: In this paper we propose a new approach for the analysis of experimental data based on the fractional Lévy stable motion (FLSM) and apply it to the Golding–Cox mRNA dataset. The FLSM takes into account non-Gaussian α-stable distributions and is characterized by the memory parameter d=H−1/α, where H is the Hurst exponent. The sign of d indicates the type of diffusion: d=0 for Lévy 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 Lévy-diffusion, but none of them is superdiffusive. We also justify presence of the non-Gaussian α-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.

Keywords: Subdiffusion; Superdiffusion; Stable distribution; Random trajectory (search for similar items in EconPapers)
Date: 2022
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Citations: View citations in EconPapers (1)

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Persistent link: https://EconPapers.repec.org/RePEc:eee:chsofr:v:154:y:2022:i:c:s0960077921009607

DOI: 10.1016/j.chaos.2021.111606

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