{
  "id": "1611.02473",
  "version": "v1",
  "published": "2016-11-08T11:00:57.000Z",
  "updated": "2016-11-08T11:00:57.000Z",
  "title": "Uniform convergence to the Q-process",
  "authors": [
    "Nicolas Champagnat",
    "Denis Villemonais"
  ],
  "comment": "8 pages",
  "categories": [
    "math.PR"
  ],
  "abstract": "The first aim of the present note is to quantify the speed of convergence of a conditioned process toward its Q-process under suitable assumptions on the quasi-stationary distribution of the process. Conversely, we prove that, if a conditioned process converges uniformly to a conservative Markov process which is itself ergodic, then it admits a unique quasi-stationary distribution and converges toward it exponentially fast, uniformly in its initial distribution. As an application, we provide a conditional ergodic theorem.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2016-11-08T11:00:57.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "60J25",
      "37A25",
      "60B10"
    ],
    "keywords": [
      "uniform convergence",
      "unique quasi-stationary distribution",
      "conditional ergodic theorem",
      "conservative markov process",
      "first aim"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 8,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}