On Hilfer's objection to the fractional time diffusion equation

E. Barkai and I.M. Sokolov

Physica A: Statistical Mechanics and its Applications, 2007, vol. 373, issue C, 231-236

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.

Keywords: Continuous time random walks; Fractional diffusion equation; Continuum limit (search for similar items in EconPapers)
Date: 2007
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Persistent link: https://EconPapers.repec.org/RePEc:eee:phsmap:v:373:y:2007:i:c:p:231-236

DOI: 10.1016/j.physa.2006.05.022

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