{
  "id": "1001.2413",
  "version": "v1",
  "published": "2010-01-14T10:52:05.000Z",
  "updated": "2010-01-14T10:52:05.000Z",
  "title": "Branching processes in random environment which extinct at a given moment",
  "authors": [
    "C. Boeinghoff",
    "E. E. Dyakonova",
    "G. Kersting",
    "V. A. Vatutin"
  ],
  "comment": "21 pages; submitted to Markov Processes and Related Fields",
  "journal": "Markov Process. Related Fields 16 (2010), no. 2, 329-350",
  "categories": [
    "math.PR"
  ],
  "abstract": "Let ${Z_{n},n\\geq 0} $ be a critical branching process in random environment and let $T$ be its moment of extinction. Under the annealed approach we prove, as $n\\to \\infty ,$ a limit theorem for the number of particles in the process at moment $n$ given $T=n+1$ and a functional limit theorem for the properly scaled process ${Z_{nt},\\delta \\leq t\\leq 1-\\delta} $ given $T=n+1$ and $\\delta \\in (0,1/2)$.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2010-01-14T10:52:05.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "60J80",
      "60G50",
      "60F17"
    ],
    "keywords": [
      "random environment",
      "branching processes",
      "functional limit theorem",
      "extinction",
      "critical branching process"
    ],
    "tags": [
      "journal article"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 21,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}