{
  "id": "cond-mat/0701126",
  "version": "v3",
  "published": "2007-01-06T18:14:39.000Z",
  "updated": "2007-05-01T17:02:29.000Z",
  "title": "Continuous time random walk and parametric subordination in fractional diffusion",
  "authors": [
    "Rudolf Gorenflo",
    "Francesco Mainardi",
    "Alessandro Vivoli"
  ],
  "comment": "28 pages, 18 figures. Workshop 'In Search of a Theory of Complexity'. Denton, Texas, August 2005",
  "journal": "Chaos, Solitons and Fractals, Vol. 34 (2007), pp. 89-103",
  "categories": [
    "cond-mat.stat-mech",
    "math-ph",
    "math.MP",
    "math.PR"
  ],
  "abstract": "The well-scaled transition to the diffusion limit in the framework of the theory of continuous-time random walk (CTRW)is presented starting from its representation as an infinite series that points out the subordinated character of the CTRW itself. We treat the CTRW as a combination of a random walk on the axis of physical time with a random walk in space, both walks happening in discrete operational time. In the continuum limit we obtain a generally non-Markovian diffusion process governed by a space-time fractional diffusion equation. The essential assumption is that the probabilities for waiting times and jump-widths behave asymptotically like powers with negative exponents related to the orders of the fractional derivatives. By what we call parametric subordination, applied to a combination of a Markov process with a positively oriented L\\'evy process, we generate and display sample paths for some special cases.",
  "revisions": [
    {
      "version": "v3",
      "updated": "2007-05-01T17:02:29.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "continuous time random walk",
      "parametric subordination",
      "space-time fractional diffusion equation",
      "continuous-time random walk",
      "non-markovian diffusion process"
    ],
    "tags": [
      "journal article"
    ],
    "publication": {
      "doi": "10.1016/j.chaos.2007.01.052",
      "journal": "Chaos Solitons and Fractals",
      "year": 2007,
      "month": "Oct",
      "volume": 34,
      "number": 1,
      "pages": 87
    },
    "note": {
      "typesetting": "TeX",
      "pages": 28,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2007CSF....34...87G"
    }
  }
}