{
  "id": "1706.03874",
  "version": "v1",
  "published": "2017-06-13T00:04:11.000Z",
  "updated": "2017-06-13T00:04:11.000Z",
  "title": "Precise large deviation estimates for branching process in random environment",
  "authors": [
    "Dariusz Buraczewski",
    "Piotr Dyszewski"
  ],
  "comment": "28 pages",
  "categories": [
    "math.PR"
  ],
  "abstract": "We consider the branching process in random environment $\\{Z_n\\}_{n\\geq 0}$, which is a~population growth process where individuals reproduce independently of each other with the reproduction law randomly picked at each generation. We describe precise asymptotics of upper large deviations, i.e. $\\mathbb{P}[Z_n > e^{\\rho n}]$. Moreover in the subcritical case, under the Cram\\'er condition on the mean of the reproduction law, we investigate large deviations-type estimates for the first passage time of the branching process in question and its total population size.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2017-06-13T00:04:11.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "60J80",
      "60F10"
    ],
    "keywords": [
      "precise large deviation estimates",
      "branching process",
      "random environment",
      "reproduction law",
      "first passage time"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 28,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}