{
  "id": "1410.1638",
  "version": "v1",
  "published": "2014-10-07T08:26:53.000Z",
  "updated": "2014-10-07T08:26:53.000Z",
  "title": "The criterion for uniqueness of quasi-stationary distributions of Markov processes and their domain of attraction problem",
  "authors": [
    "Hanjun Zhang",
    "Pengwen Guo",
    "Yixia Zhu"
  ],
  "comment": "14pages",
  "categories": [
    "math.PR"
  ],
  "abstract": "We consider a Markov process $ X(t) $ on the nonnegative integers $E= S \\cup \\{0\\}$, where $S=\\{1,2,\\ldots\\}$ is an irreducible class and 0 is an absorbing state. In this paper, we investigate conditions under which the quasi-stationary distribution for $X(t)$ exists and is unique, and any initial distribution supported in $S$ is in the domain of attraction of this quasi-stationary distribution. We further find five conditions which are equivalent to that the extinction time is uniformly bounded. As a consequence, we prove the van Doorn's conjecture in \\cite{VD2012}. And we can greatly improve theorem 1 in \\cite{VD2012}.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2014-10-07T08:26:53.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "60J27",
      "60J80"
    ],
    "keywords": [
      "quasi-stationary distribution",
      "markov processes",
      "attraction problem",
      "uniqueness",
      "van doorns conjecture"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 14,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2014arXiv1410.1638Z"
    }
  }
}