Phys. Rev. E 69, 011107 (2004) - Uncoupled continuous-time random walks: Solution and limiting behavior of the master equation

Uncoupled continuous-time random walks: Solution and limiting behavior of the master equation

Enrico Scalas, Rudolf Gorenflo, and Francesco Mainardi

Phys. Rev. E 69, 011107 – Published 30 January 2004

Abstract

A detailed study is presented for a large class of uncoupled continuous-time random walks. The master equation is solved for the Mittag-Leffler survival probability. The properly scaled diffusive limit of the master equation is taken and its relation with the fractional diffusion equation is discussed. Finally, some common objections found in the literature are thoroughly reviewed.

Received 4 September 2003

DOI:https://doi.org/10.1103/PhysRevE.69.011107

©2004 American Physical Society

Authors & Affiliations

Enrico Scalas^*

Department of Advanced Sciences and Technologies, East Piedmont University, Corso Borsalino 54, I-15100 Alessandria, Italy

Rudolf Gorenflo

First Mathematical Institute, Free University of Berlin, Arnimallee 2-6, D-14195 Berlin, Germany

Francesco Mainardi

Department of Physics, Bologna University and INFN Bologna, via Irnerio 46, I-40126 Bologna, Italy

^*Electronic address: scalas@unipmn.it; URL: http://www.fracalmo.org

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Vol. 69, Iss. 1 — January 2004

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