{
  "id": "1703.01960",
  "version": "v1",
  "published": "2017-03-06T16:39:03.000Z",
  "updated": "2017-03-06T16:39:03.000Z",
  "title": "A general approach to branching processes in varying environment",
  "authors": [
    "Götz Kersting"
  ],
  "comment": "22 pages",
  "categories": [
    "math.PR"
  ],
  "abstract": "Branching processes $(Z_n)_{n \\ge 0}$ in varying environment generalize the Galton-Watson process, in that they allow time-dependence of the offspring distribution. Our main results are general criteria for a.s. extinction and square-integrability of the martingale $(Z_n/\\mathbf E[Z_n])_{n \\ge 0}$ as well as Yaglom type result stating convergence in distribution of the suitably normalized population size $Z_n$, conditioned on the event $Z_n >0$.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2017-03-06T16:39:03.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "60J80"
    ],
    "keywords": [
      "branching processes",
      "varying environment",
      "general approach",
      "yaglom type result stating convergence",
      "general criteria"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 22,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}