{
  "id": "1409.8067",
  "version": "v1",
  "published": "2014-09-29T10:51:22.000Z",
  "updated": "2014-09-29T10:51:22.000Z",
  "title": "Existence and construction of quasi-stationary distributions for one-dimensional diffusions",
  "authors": [
    "Hanjun Zhang",
    "Guoman He"
  ],
  "comment": "9 pages",
  "categories": [
    "math.PR"
  ],
  "abstract": "In this paper, we study quasi-stationary distributions (QSDs) for one-dimensional diffusions killed at 0, when 0 is a regular boundary and $+\\infty$ is a natural boundary. More precisely, we not only give a necessary and sufficient condition for the existence of a QSD, but also we construct all QSDs for one-dimensional diffusions. Moreover, we give a sufficient condition for $R$-positivity of the process killed at the origin. This condition is only based on the drift, which is easy to check.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2014-09-29T10:51:22.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "60J60",
      "60J70",
      "37A30"
    ],
    "keywords": [
      "sufficient condition",
      "construction",
      "study quasi-stationary distributions",
      "regular boundary",
      "natural boundary"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 9,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2014arXiv1409.8067Z"
    }
  }
}