{
  "id": "1412.3281",
  "version": "v1",
  "published": "2014-12-10T12:44:20.000Z",
  "updated": "2014-12-10T12:44:20.000Z",
  "title": "Space-fractional versions of the negative binomial and Polya-type processes",
  "authors": [
    "L. Beghin",
    "P. Vellaisamy"
  ],
  "comment": "12 pages",
  "categories": [
    "math.PR"
  ],
  "abstract": "In this paper, we introduce a space fractional negative binomial (SFNB) process by subordinating the space fractional Poisson process to a gamma process. Its one-dimensional distributions are derived in terms of generalized Wright functions and their governing equations are obtained. It is a L\\'evy process and the corresponding L\\'evy measure is given. Extensions to the case of distributed order SFNB process, where the fractional index follows a two-point distribution, is analyzed in detail. Finally, the connections of the SFNB process to a space fractional Polya-type process is also pointed out.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2014-12-10T12:44:20.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "60G22",
      "60G51",
      "60E05"
    ],
    "keywords": [
      "polya-type processes",
      "space-fractional versions",
      "space fractional polya-type process",
      "space fractional poisson process",
      "space fractional negative binomial"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 12,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2014arXiv1412.3281B"
    }
  }
}