{
  "id": "1109.1849",
  "version": "v2",
  "published": "2011-09-08T21:27:38.000Z",
  "updated": "2013-09-30T21:50:25.000Z",
  "title": "Supercritical branching diffusions in random environment",
  "authors": [
    "Martin Hutzenthaler"
  ],
  "comment": "11 pages",
  "journal": "Elec. Comm. in Probab. 16 (2011), 781--791",
  "doi": "10.1214/ECP.v16-1685",
  "categories": [
    "math.PR"
  ],
  "abstract": "Supercritical branching processes in constant environment conditioned on eventual extinction are known to be subcritical branching processes. The case of random environment is more subtle. A supercritical branching diffusion in random environment (BDRE) conditioned on eventual extinction of the population is not a BDRE. However the quenched law of the population size of a supercritical BDRE conditioned on eventual extinction is equal to the quenched law of the population size of a subcritical BDRE. As a consequence, supercritical BDREs have a phase transition which is similar to a well-known phase transition of subcritical branching processes in random environment.",
  "revisions": [
    {
      "version": "v2",
      "updated": "2013-09-30T21:50:25.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "random environment",
      "supercritical branching diffusion",
      "eventual extinction",
      "subcritical branching processes",
      "supercritical bdre"
    ],
    "tags": [
      "journal article"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 11,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2011arXiv1109.1849H"
    }
  }
}