{
  "id": "math/0609518",
  "version": "v2",
  "published": "2006-09-19T09:32:21.000Z",
  "updated": "2007-10-15T09:59:12.000Z",
  "title": "Changing the branching mechanism of a continuous state branching process using immigration",
  "authors": [
    "Romain Abraham",
    "Jean-Francois Delmas"
  ],
  "journal": "Annales de l'Institut Henri Poincare (B) Probability and Statistics 45, 1 (2009) 226-238",
  "doi": "10.1214/07-AIHP165",
  "categories": [
    "math.PR"
  ],
  "abstract": "We construct a continuous state branching process with immigration (CBI) whose immigration depends on the CBI itself and we recover a continuous state branching process (CB). This provides a dual construction of the pruning at nodes of CB introduced by the authors in a previous paper. This construction is a natural way to model neutral mutation. Using exponential formula, we compute the probability of extinction of the original type population in a critical or sub-critical quadratic branching, conditionally on the non extinction of the total population.",
  "revisions": [
    {
      "version": "v2",
      "updated": "2007-10-15T09:59:12.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "continuous state branching process",
      "branching mechanism",
      "original type population",
      "model neutral mutation",
      "immigration depends"
    ],
    "tags": [
      "journal article"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2009AnIHP..45..226A"
    }
  }
}