On Hilfer's objection to the fractional time diffusion equation

E. Barkai, I. M. Sokolov

Research output: Contribution to journalArticlepeer-review

9 Scopus citations

Abstract

Hilfer [Physica A 329 (2003) 35] claims to give an example of a continuous time random walk (CTRW) model with long-tailed waiting time probability density that approaches a Gaussian behavior in the continuum limit. Rigorous limit theorems, derived previously, show however that in the limit of long-time such a CTRW converges to a non-Gaussian behavior. We discuss two types of continuum limits for the CTRW model: the fractional continuum limit and the one introduced by Hilfer. We show that the fractional limit yields the correct long-time behavior of the CTRW, while Hilfer's continuum limit does not. We discuss a general approach to find a continuum limit of the CTRW process.

Original languageEnglish
Pages (from-to)231-236
Number of pages6
JournalPhysica A: Statistical Mechanics and its Applications
Volume373
DOIs
StatePublished - 1 Jan 2007

Bibliographical note

Funding Information:
EB thank the Israel Science Foundation and the center of complexity in Jerusalem, for financial support.

Keywords

  • Continuous time random walks
  • Continuum limit
  • Fractional diffusion equation

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