Quantum mechanics

Linguistics

Philosophy

Service (business)

Statistics

Markov process

Variety (cybernetics)

Brownian motion

Anomalous diffusion

Applied mathematics

Economics

Computer science

Statistical physics

Relation (database)

Physics

Diffusion

Database

Mathematics

Diffusion process

Mathematical analysis

Innovation diffusion

Fick's laws of diffusion

Subordination (linguistics)

Continuous-time random walk

Economy

Diffusion equation

Knowledge management

Random walk

Physical review. E

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.

Relation between generalized diffusion equations and subordination schemes