{
  "id": "1811.04567",
  "version": "v1",
  "published": "2018-11-12T05:59:13.000Z",
  "updated": "2018-11-12T05:59:13.000Z",
  "title": "Time-changed Poisson processes of order $k$",
  "authors": [
    "Ayushi S. Sengar",
    "A. Maheshwari",
    "N. S. Upadhye"
  ],
  "comment": "19 Pages, 6 figures",
  "categories": [
    "math.PR"
  ],
  "abstract": "In this article, we study the Poisson process of order k (PPoK) time-changed with an independent L\\'evy subordinator and its inverse, which we call respectively, as TCPPoK-I and TCPPoK-II, through various distributional properties, long-range dependence and limit theorems for the PPoK and the TCPPoK-I. Further, we study the governing difference-differential equations of the TCPPoK-I for the case inverse Gaussian subordinator. Similarly, we study the distributional properties, asymptotic moments and the governing difference-differential equation of TCPPoK-II. As an application to ruin theory, we give a governing differential equation of ruin probability in insurance ruin using these processes. Finally, we present some simulated sample paths of both the processes.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2018-11-12T05:59:13.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "60G55",
      "60G51"
    ],
    "keywords": [
      "time-changed poisson processes",
      "governing difference-differential equation",
      "case inverse gaussian subordinator",
      "distributional properties",
      "independent levy subordinator"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 19,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}