{
  "id": "1906.00373",
  "version": "v1",
  "published": "2019-06-02T09:23:18.000Z",
  "updated": "2019-06-02T09:23:18.000Z",
  "title": "On aggregation of subcritical Galton-Watson branching processes with regularly varying immigration",
  "authors": [
    "Matyas Barczy",
    "Fanni K. Nedényi",
    "Gyula Pap"
  ],
  "comment": "42 pages",
  "categories": [
    "math.PR"
  ],
  "abstract": "We study an iterated temporal and contemporaneous aggregation of $N$ independent copies of a strongly stationary subcritical Galton-Watson branching process with regularly varying immigration having index $\\alpha \\in (0, 2)$. Limits of finite dimensional distributions of appropriately centered and scaled aggregated partial sum processes are shown to exist when first taking the limit as $N \\to \\infty$ and then the time scale $n \\to \\infty$. The limit process is an $\\alpha$-stable process if $\\alpha \\in (0, 1) \\cup (1, 2)$, and a deterministic line with slope $1$ if $\\alpha = 1$.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2019-06-02T09:23:18.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "60J80",
      "60F05",
      "60G10",
      "60G52",
      "60G70"
    ],
    "keywords": [
      "regularly varying immigration",
      "aggregation",
      "scaled aggregated partial sum processes",
      "stationary subcritical galton-watson branching process"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 42,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}