Continuous time random walk, Mittag-Leffler waiting time and fractional diffusion: mathematical aspects

Simple item page
dc.creatorGorenflo, Rudolf
dc.creatorMainardi, Francesco
dc.date2007-05-06
dc.date2008-05-12
dc.date.accessioned2026-07-07T09:39:12Z
dc.date.available2026-07-07T09:39:12Z
dc.descriptionWe show the asymptotic long-time equivalence of a generic power law waiting time distribution to the Mittag-Leffler waiting time distribution, characteristic for a time fractional CTRW. This asymptotic equivalence is effected by a combination of "rescaling" time and "respeeding" the relevant renewal process followed by a passage to a limit for which we need a suitable relation between the parameters of rescaling and respeeding. Turning our attention to spatially 1-D CTRWs with a generic power law jump distribution, "rescaling" space can be interpreted as a second kind of "respeeding" which then, again under a proper relation between the relevant parameters leads in the limit to the space-time fractional diffusion equation. Finally, we treat the `time fractional drift" process as a properly scaled limit of the counting number of a Mittag-Leffler renewal process.
dc.description36 pages, 3 figures (5 files eps). Invited lecture by R. Gorenflo at the 373. WE-Heraeus-Seminar on Anomalous Transport: Experimental Results and Theoretical Challenges, Physikzentrum Bad-Honnef (Germany), 12-16 July 2006; Chairmen: R. Klages, G. Radons and I.M. Sokolov
dc.identifierhttps://arxiv.org/abs/0705.0797
dc.identifierhttp://arxiv.org/abs/0705.0797
dc.identifier"Anomalous Transport: Foundations and Applications", edited by R. Klages, G. Radons and I.M Sokolov, as Chapter 4, pp. 93-127,WILEY-VCH, Weinheim, Germany (2008) [ISBN 978-3-5277-40722-4]
dc.identifier.urihttp://salesiana.dossiersoluciones.com/handle/123456789/161081
dc.subjectStatistical Mechanics
dc.subjectDisordered Systems and Neural Networks
dc.subjectMathematical Physics
dc.titleContinuous time random walk, Mittag-Leffler waiting time and fractional diffusion: mathematical aspects
dc.typetext

Files

Collections

arXiv