Stochastic foundations of $g$-subdiffusion process
Statistical Mechanics
2021-10-20 v1
Abstract
Recently, in the paper: T. Koszto{\l}owicz and A. Dutkiewicz, Phys. Rev. E \textbf{104}, 014118 (2021) the --subdiffusion equation with fractional Caputo time derivative with respect to another function has been considered. This equation offers new possibilities for modelling diffusion such as a process in which a type of diffusion evolves continuously over time. However, the equation has not been derived from a stochastic model and the stochastic interpretation of --subdiffusion has been unknown. In this paper we show stochastic foundations of this process. We derive the equation by means of a modified Continuous Time Random Walk model. Interpretation of the --subdiffusion process is also discussed.
Cite
@article{arxiv.2107.10532,
title = {Stochastic foundations of $g$-subdiffusion process},
author = {Tadeusz Kosztołowicz and Aldona Dutkiewicz},
journal= {arXiv preprint arXiv:2107.10532},
year = {2021}
}
Comments
4 pages