TY  - JOUR
A1  - Chechkin, Aleksei V.
A1  - Sokolov, Igor M.
T1  - Relation between generalized diffusion equations and subordination schemes
T2  - Physical review : E, Statistical, nonlinear and soft matter physics
N2  - Generalized (non-Markovian) diffusion equations with different memory kernels and subordination schemes based on random time change in the Brownian diffusion process are popular mathematical tools for description of a variety of non-Fickian diffusion processes in physics, biology, and earth sciences. Some of such processes (notably, the fluid limits of continuous time random walks) allow for either kind of description, but other ones do not. In the present work we discuss the conditions under which a generalized diffusion equation does correspond to a subordination scheme, and the conditions under which a subordination scheme does possess the corresponding generalized diffusion equation. Moreover, we discuss examples of random processes for which only one, or both kinds of description are applicable.
Y1  - 2021
UR  - https://publishup.uni-potsdam.de/frontdoor/index/index/docId/61185
SN  - 2470-0045
SN  - 2470-0053
VL  - 103
IS  - 3
PB  - American Physical Society
CY  - College Park
ER  -