{
  "id": "1310.3161",
  "version": "v1",
  "published": "2013-10-11T15:16:42.000Z",
  "updated": "2013-10-11T15:16:42.000Z",
  "title": "Fractional Poisson processes and their representation by infinite systems of ordinary differential equations",
  "authors": [
    "Markus Kreer",
    "Ayse Kizilersu",
    "Anthony W. Thomas"
  ],
  "comment": "15 pages",
  "journal": "Statistics and Probability Letters84 (2014), pp. 27-32",
  "doi": "10.1016/j.spl.2013.09.028",
  "categories": [
    "math.CA",
    "math.PR",
    "stat.ME"
  ],
  "abstract": "Fractional Poisson processes, a rapidly growing area of non-Markovian stochastic processes, are useful in statistics to describe data from counting processes when waiting times are not exponentially distributed. We show that the fractional Kolmogorov-Feller equations for the probabilities at time t can be representated by an infinite linear system of ordinary differential equations of first order in a transformed time variable. These new equations resemble a linear version of the discrete coagulation-fragmentation equations, well-known from the non-equilibrium theory of gelation, cluster-dynamics and phase transitions in physics and chemistry.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2013-10-11T15:16:42.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "ordinary differential equations",
      "fractional poisson processes",
      "infinite systems",
      "representation",
      "discrete coagulation-fragmentation equations"
    ],
    "tags": [
      "journal article"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 15,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2013arXiv1310.3161K"
    }
  }
}