{
  "id": "2304.10487",
  "version": "v1",
  "published": "2023-04-20T17:31:10.000Z",
  "updated": "2023-04-20T17:31:10.000Z",
  "title": "Generalized Fractional Negative Binomial Process",
  "authors": [
    "Ritik Soni",
    "Ashok Kumar Pathak"
  ],
  "categories": [
    "math.PR"
  ],
  "abstract": "In this paper, we introduce a generalized fractional negative binomial process (GFNBP) by time changing the fractional Poisson process with an independent Mittag-Leffler (ML) Levy subordinator. We study its distributional properties and its connection to PDEs. We examine the long-range dependence (LRD) property of the GFNBP and show that it is not infinitely divisible. The space fractional and the non-homogeneous variants of the GFNBP are explored. Finally, simulated sample paths for the ML Levy subordinator and the GFNBP are also presented.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2023-04-20T17:31:10.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "60G22",
      "60G51",
      "60G55",
      "60E05"
    ],
    "keywords": [
      "generalized fractional negative binomial process",
      "ml levy subordinator",
      "fractional poisson process",
      "independent mittag-leffler",
      "simulated sample paths"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}