{
  "id": "1304.0189",
  "version": "v1",
  "published": "2013-03-31T11:20:40.000Z",
  "updated": "2013-03-31T11:20:40.000Z",
  "title": "Fractional Non-Linear, Linear and Sublinear Death Processes",
  "authors": [
    "Enzo Orsingher",
    "Federico Polito",
    "Ludmila Sakhno"
  ],
  "journal": "Journal of Statistical Physics, Vol. 141 (1), 68-93, 2010",
  "doi": "10.1007/s10955-010-0045-2",
  "categories": [
    "math.PR"
  ],
  "abstract": "This paper is devoted to the study of a fractional version of non-linear $\\mathpzc{M}^\\nu(t)$, $t>0$, linear $M^\\nu (t)$, $t>0$ and sublinear $\\mathfrak{M}^\\nu (t)$, $t>0$ death processes. Fractionality is introduced by replacing the usual integer-order derivative in the difference-differential equations governing the state probabilities, with the fractional derivative understood in the sense of Dzhrbashyan--Caputo. We derive explicitly the state probabilities of the three death processes and examine the related probability generating functions and mean values. A useful subordination relation is also proved, allowing us to express the death processes as compositions of their classical counterparts with the random time process $T_{2 \\nu} (t)$, $t>0$. This random time has one-dimensional distribution which is the folded solution to a Cauchy problem of the fractional diffusion equation.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2013-03-31T11:20:40.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "sublinear death processes",
      "fractional non-linear",
      "state probabilities",
      "fractional diffusion equation",
      "random time process"
    ],
    "tags": [
      "journal article"
    ],
    "publication": {
      "journal": "Journal of Statistical Physics",
      "year": 2010,
      "month": "Oct",
      "volume": 141,
      "number": 1,
      "pages": 68
    },
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2010JSP...141...68O"
    }
  }
}