{
  "id": "1409.8094",
  "version": "v1",
  "published": "2014-09-29T12:21:51.000Z",
  "updated": "2014-09-29T12:21:51.000Z",
  "title": "Existence and uniqueness of mean-ratio quasi-stationary distribution for one-dimensional diffusions",
  "authors": [
    "Hanjun Zhang",
    "Guoman He"
  ],
  "comment": "7 pages",
  "categories": [
    "math.PR"
  ],
  "abstract": "In this paper, we study mean-ratio quasi-stationary distribution (MRQSD) for one-dimensional diffusion $X$ killed at 0, when $+\\infty$ is an entrance boundary and 0 is an exit boundary. More precisely, we not only show that the process is $R$-positive, but also prove the existence and uniqueness of MRQSD by using the spectral theory tool. As a consequence, this unique MRQSD is just the stationary distribution of $Q$-process.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2014-09-29T12:21:51.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "60J60",
      "60J70",
      "37A30"
    ],
    "keywords": [
      "one-dimensional diffusion",
      "uniqueness",
      "study mean-ratio quasi-stationary distribution",
      "spectral theory tool",
      "unique mrqsd"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 7,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2014arXiv1409.8094H"
    }
  }
}