{
  "id": "1504.04997",
  "version": "v1",
  "published": "2015-04-20T10:08:37.000Z",
  "updated": "2015-04-20T10:08:37.000Z",
  "title": "Decomposable branching processes having a fixed extinction moment",
  "authors": [
    "Vladimir Vatutin",
    "Elena Dyakonova"
  ],
  "comment": "28 pages",
  "categories": [
    "math.PR"
  ],
  "abstract": "The asymptotic behavior, as $n\\rightarrow \\infty $ of the probability of the event that a decomposable critical branching process $\\mathbf{Z}(m)=(Z_{1}(m),...,Z_{N}(m)),$ $m=0,1,2,...,$ with $N$ types of particles dies at moment $n$ is investigated and conditional limit theorems are proved describing the distribution of the number of particles in the process $\\mathbf{Z}(\\cdot)$ at moment $m<n,$ given that the extinction moment of the process is $n$. These limit theorems may be considered as the statements describing the distribution of the number of vertices in the layers of certain classes of simply generated random trees having a fixed hight.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2015-04-20T10:08:37.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "60J80",
      "60F99",
      "92D25"
    ],
    "keywords": [
      "fixed extinction moment",
      "decomposable branching processes",
      "conditional limit theorems",
      "asymptotic behavior",
      "particles dies"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 28,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2015arXiv150404997V"
    }
  }
}