{
  "id": "1610.02532",
  "version": "v1",
  "published": "2016-10-08T13:48:51.000Z",
  "updated": "2016-10-08T13:48:51.000Z",
  "title": "On uniform closeness of local times of Markov chains and i.i.d. sequences",
  "authors": [
    "Diego F. de Bernardini",
    "Christophe Gallesco",
    "Serguei Popov"
  ],
  "comment": "39 pages, 1 figure",
  "categories": [
    "math.PR"
  ],
  "abstract": "In this paper we use the soft local time technique to obtain a coupling between the field of local times at time $n$ of a Markov chain, and the one of a sequence of $n$ i.i.d. random variables with law given by the invariant measure of that Markov chain. As a result, we obtain upper bounds on the total variation distance between the two fields, which are uniform in $n$.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2016-10-08T13:48:51.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "60J05",
      "60G09",
      "60J55"
    ],
    "keywords": [
      "markov chain",
      "uniform closeness",
      "soft local time technique",
      "total variation distance",
      "invariant measure"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 39,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}