{
  "id": "2409.07044",
  "version": "v1",
  "published": "2024-09-11T06:25:48.000Z",
  "updated": "2024-09-11T06:25:48.000Z",
  "title": "Tempered space-time fractional negative binomial process",
  "authors": [
    "Shilpa",
    "Ashok Kumar Pathak",
    "Aditya Maheshwari"
  ],
  "comment": "11 pages",
  "categories": [
    "math.PR"
  ],
  "abstract": "In this paper, we define a tempered space-time fractional negative binomial process (TSTFNBP) by subordinating the fractional Poisson process with an independent tempered Mittag-Leffler L\\'{e}vy subordinator. We study its distributional properties and its connection to partial differential equations. We derive the asymptotic behavior of its fractional order moments and long-range dependence property. It is shown that the TSTFNBP exhibits overdispersion. We also obtain some results related to the first-passage time.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2024-09-11T06:25:48.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "60G22",
      "60G51"
    ],
    "keywords": [
      "space-time fractional negative binomial process",
      "tempered space-time fractional negative binomial",
      "fractional poisson process",
      "partial differential equations",
      "fractional order moments"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 11,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}