{
  "id": "1305.3074",
  "version": "v2",
  "published": "2013-05-14T09:23:09.000Z",
  "updated": "2016-01-13T19:19:01.000Z",
  "title": "On the fractional Poisson process and the discretized stable subordinator",
  "authors": [
    "Rudolf Gorenflo",
    "Francesco Mainardi"
  ],
  "comment": "30 pages, 4 figures. A preliminary version of this paper was an invited talk given by R. Gorenflo at the Conference ICMS2011, held at the International Centre of Mathematical Sciences, Pala-Kerala (India) 3-5 January 2011, devoted to Prof Mathai on the occasion of his 75 birthday",
  "journal": "AXIOMS Vol. 4, pp 321-344 (2015)",
  "doi": "10.3390/axioms4030321",
  "categories": [
    "math.PR",
    "math-ph",
    "math.MP"
  ],
  "abstract": "The fractional Poisson process and the Wright process (as discretization of the stable subordinator) along with their diffusion limits play eminent roles in theory and simulation of fractional diffusion processes. Here we have analyzed these two processes, concretely the corresponding counting number and Erlang processes, the latter being the processes inverse to the former. Furthermore we have obtained the diffusion limits of all these processes by well-scaled refinement of waiting times and jumps",
  "revisions": [
    {
      "version": "v1",
      "updated": "2013-05-14T09:23:09.000Z",
      "comment": "29 pages, 4 figures. This paper is based on an invited talk given by R. Gorenflo at the Conference ICMS2011, held at the International Centre of Mathematical Sciences, Pala-Kerala (India) 3-5 January 2011, devoted to Prof Mathai on the occasion of his 75 birthday",
      "journal": null,
      "doi": null
    },
    {
      "version": "v2",
      "updated": "2016-01-13T19:19:01.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "26A33",
      "33E12",
      "45K05",
      "60G18",
      "60G50",
      "60G52",
      "60K05",
      "76R50"
    ],
    "keywords": [
      "fractional poisson process",
      "discretized stable subordinator",
      "diffusion limits play eminent roles",
      "fractional diffusion processes"
    ],
    "tags": [
      "conference paper",
      "journal article"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 30,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2013arXiv1305.3074G"
    }
  }
}