{
  "id": "1706.05747",
  "version": "v1",
  "published": "2017-06-19T00:04:44.000Z",
  "updated": "2017-06-19T00:04:44.000Z",
  "title": "Convergence to a Continuous State Branching Process with jumps and Height Process",
  "authors": [
    "Ibrahima Drame",
    "Etienne Pardoux"
  ],
  "categories": [
    "math.PR"
  ],
  "abstract": "In this work, we study asymptotics of the genealogy of Galton-Watson processes. Thus we consider a offspring distribution such that the rescaled Galton-Watson processes converges to a continuous state branching process (CSBP) with jumps. After we show that the rescaled height (or exploration) process of the corresponding Galton-Watson family tree, converges in a functional sense, to the continuous height process that Le Gall and Le Jan introduced in 1998 on their paper \"branching processes in L\\'evy processes : The exploration process\".",
  "revisions": [
    {
      "version": "v1",
      "updated": "2017-06-19T00:04:44.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "continuous state branching process",
      "convergence",
      "rescaled galton-watson processes converges",
      "exploration process",
      "levy processes"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}