{
  "id": "1712.08892",
  "version": "v1",
  "published": "2017-12-24T08:59:06.000Z",
  "updated": "2017-12-24T08:59:06.000Z",
  "title": "Asymptotic Behaviors for Critical Branching Processes with Immigration",
  "authors": [
    "Doudou Li",
    "Mei Zhang"
  ],
  "categories": [
    "math.PR"
  ],
  "abstract": "In this paper, we investigate the asymptotic behaviors of the critical branching process with immigration $\\{Z_n, n\\ge 0\\}$. First we get some estimation for the probability generating function of $Z_n$. Based on it, we get a large deviation for $Z_{n+1}/Z_n$. Lower and upper deviations for $Z_n$ are also studied. As a by-product, an upper deviation for $\\max_{1\\le i\\le n} Z_i$ is obtained.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2017-12-24T08:59:06.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "critical branching process",
      "asymptotic behaviors",
      "immigration",
      "upper deviation",
      "probability generating function"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}