Anomalous diffusion. A competition between the very large jumps in physical and operational times

TL;DR

This paper investigates anomalous diffusion by coupling large jumps in physical and operational times using Levy-stable processes, revealing both subdiffusive and superdiffusive behaviors through subordination techniques.

Contribution

It introduces a novel approach to model anomalous diffusion by coupling physical and operational times via Levy-stable processes, highlighting different diffusion regimes.

Findings

Identification of subdiffusive and superdiffusive regimes

Use of subordination of Levy-stable processes

Analysis of two-power-law relaxation patterns

Abstract

In this paper we analyze a coupling between the very large jumps in physical and operational times as applied to anomalous diffusion. The approach is based on subordination of a skewed Levy-stable process by its inverse to get two types of operational time - the spent and the residual waiting time, respectively. The studied processes have different properties which display both subdiffusive and superdiffusive features of anomalous diffusion underlying the two-power-law relaxation patterns.