{
  "id": "0705.0797",
  "version": "v2",
  "published": "2007-05-06T10:38:26.000Z",
  "updated": "2008-05-12T14:31:10.000Z",
  "title": "Continuous time random walk, Mittag-Leffler waiting time and fractional diffusion: mathematical aspects",
  "authors": [
    "Rudolf Gorenflo",
    "Francesco Mainardi"
  ],
  "comment": "36 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",
  "journal": "\"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]",
  "categories": [
    "cond-mat.stat-mech",
    "cond-mat.dis-nn",
    "math-ph",
    "math.MP"
  ],
  "abstract": "We 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.",
  "revisions": [
    {
      "version": "v2",
      "updated": "2008-05-12T14:31:10.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "continuous time random walk",
      "mittag-leffler waiting time",
      "fractional diffusion",
      "power law jump distribution",
      "law waiting time distribution"
    ],
    "tags": [
      "journal article"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 36,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2007arXiv0705.0797G"
    }
  }
}