{
  "id": "1611.03010",
  "version": "v1",
  "published": "2016-11-09T16:47:35.000Z",
  "updated": "2016-11-09T16:47:35.000Z",
  "title": "Population processes with unbounded extinction rate conditioned to non-extinction",
  "authors": [
    "Nicolas Champagnat",
    "Denis Villemonais"
  ],
  "comment": "22 pages",
  "categories": [
    "math.PR"
  ],
  "abstract": "This article studies the quasi-stationary behaviour of population processes with unbounded absorption rate, including one-dimensional birth and death processes with catastrophes and multi-dimensional birth and death processes, modeling biological populations in interaction. To handle this situation, we develop original non-linear Lyapunov criteria. We obtain the exponential convergence in total variation of the conditional distributions to a unique quasi-stationary distribution, uniformly with respect to the initial distribution. Our results cover all one-dimensional birth and death processes which come down from infinity with catastrophe rate satisfying appropriate bounds, and multi-dimensional birth and death models with stronger intra-specific than inter-specific competition.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2016-11-09T16:47:35.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "60J27",
      "37A25",
      "60B10",
      "92D25",
      "92D40"
    ],
    "keywords": [
      "unbounded extinction rate",
      "population processes",
      "death processes",
      "multi-dimensional birth",
      "non-extinction"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 22,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}