Confined random motion with Laplace and Linnik statistics

Abstract

In this paper we reveal that the conjugate property of Bernstein functions connects the tempered subdiffusion with the confinement. The interpretation of anomalous diffusion tending to the confinement is that diffusive motion, accompanied by multiple-trapping events with infinite mean sojourn time, is transformed into pure jumps, restricted in confined environment. This model, just like the tempered one, is generally valid in a wide class of problems of transport in random media that include live cells, relaxation in heterogeneous substances, and jump-diffusion. A relation of our approach to the popular diffusive diffusivity is explained.