{
  "id": "1409.8103",
  "version": "v1",
  "published": "2014-09-29T12:48:44.000Z",
  "updated": "2014-09-29T12:48:44.000Z",
  "title": "Domain of attraction of the quasi-stationary distribution for one-dimensional diffusions",
  "authors": [
    "Hanjun Zhang",
    "Guoman He"
  ],
  "comment": "9 pages",
  "categories": [
    "math.PR"
  ],
  "abstract": "In this paper, we study quasi-stationarity for one-dimensional diffusions killed at 0, when 0 is a regular boundary and $+\\infty$ is an entrance boundary. We give a necessary and sufficient condition for the existence of exactly one quasi-stationary distribution, and that this distribution attracts all initial distributions. In particular, a novelty here is that we show that if the killed semigroup is intrinsically ultracontractive, then it is not only a sufficient condition ensuring the uniqueness of the quasi-stationary distribution, but also a necessary condition.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2014-09-29T12:48:44.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "60J60",
      "60J70",
      "47D07",
      "37A30"
    ],
    "keywords": [
      "quasi-stationary distribution",
      "one-dimensional diffusions",
      "sufficient condition",
      "attraction",
      "study quasi-stationarity"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 9,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2014arXiv1409.8103Z"
    }
  }
}