{
  "id": "1608.08062",
  "version": "v1",
  "published": "2016-08-29T14:18:10.000Z",
  "updated": "2016-08-29T14:18:10.000Z",
  "title": "How many families survive for a long time",
  "authors": [
    "V. A. Vatutin",
    "E. E. Dyakonova"
  ],
  "comment": "arXiv admin note: text overlap with arXiv:1603.03199",
  "categories": [
    "math.PR"
  ],
  "abstract": "A critical branching process $\\left\\{Z_{k},k=0,1,2,...\\right\\} $ in a random environment generated by a sequence of independent and identically distributed random reproduction laws is considered.\\ Let $Z_{p,n}$ be the number of particles at time $p\\leq n$ having a positive offspring number at time $n$. \\ A theorem is proved describing the limiting behavior, as $% n\\rightarrow \\infty $ of the distribution of a properly scaled process $\\log Z_{p,n}$ under the assumptions $Z_{n}>0$ and $p\\ll n$.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2016-08-29T14:18:10.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "60J80",
      "60F99"
    ],
    "keywords": [
      "long time",
      "families survive",
      "identically distributed random reproduction laws",
      "random environment",
      "offspring number"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}