Stochastic interpretation of<mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"><mml:mi>g</mml:mi></mml:math>-subdiffusion process
Tadeusz Kosztołowicz, Aldona Dutkiewicz
Abstract
Recently, we considered the g-subdiffusion equation with a fractional Caputo time derivative with respect to another function g, T. Kosztołowicz et al. [Phys. Rev. E 104, 014118 (2021)2470-004510.1103/PhysRevE.104.014118]. This equation offers different possibilities for modeling 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 g subdiffusion is still unknown. In this Letter, we show the stochastic foundations of this process. We derive the equation by means of a modified continuous time random walk model. An interpretation of the g-subdiffusion process is also discussed.