Abstract: Heterogeneous diffusion processes defined as a solution to the overdamped Langevin equation with multiplicative noise, the amplitude of which has a power-law space-dependent form, are studied. Particular emphasis is on discrete analogs of these processes, for which, in particular, an asymptotic estimate of their variance behavior in time is obtained. In addition, a class of processes formed by deformation of the discrete analog of the fractional Brownian motion using the Cantor ladder and its inverse transformation is considered. It is found that such a class turns out to be close in structure to discrete analogs of heterogeneous processes. This class of processes allows us to illustrate geometrically the emergence of sub- and superdiffusion transport regimes. On the basis of discrete analogs of heterogeneous processes and memory flow phenomenology, we construct a class of random processes that allows us to model nonlocality in time and space taking into account spatial heterogeneity.

Cite: Arkashov N.S. , Seleznev V.A.
On heterogeneous diffusion processes and the formation of spatial–temporal nonlocality
Chaos. 2023. V.33. N7. 073145 :1-10. DOI: 10.1063/5.0159907 WOS Scopus РИНЦ OpenAlex

Dates:

Submitted:	May 28, 2023
Accepted:	Jul 6, 2023
Published print:	Jul 19, 2023
Published online:	Jul 19, 2023

Identifiers:

Web of science:	WOS:001061949900001
Scopus:	2-s2.0-85165519945
Elibrary:	62254498
OpenAlex:	W4384663017

Citing:

DB	Citing
Scopus	6
OpenAlex	7
Web of science	5

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