{
  "id": "2207.13758",
  "version": "v1",
  "published": "2022-07-27T19:25:16.000Z",
  "updated": "2022-07-27T19:25:16.000Z",
  "title": "On the quenched CLT for stationary Markov chains",
  "authors": [
    "Magda Peligrad"
  ],
  "comment": "19 pages",
  "categories": [
    "math.PR"
  ],
  "abstract": "In this paper we give necessary and sufficient conditions for the almost sure central limit theorem started at a point, known under the name of quenched central limit theorem. This is possible by using a new idea of conditioning with respect to both the past and the future of the Markov chain. As applications we provide new sufficient projective conditions for the quenched CLT.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2022-07-27T19:25:16.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "60F05",
      "60F15",
      "60J05",
      "60G10"
    ],
    "keywords": [
      "stationary markov chains",
      "quenched clt",
      "sure central limit theorem",
      "quenched central limit theorem",
      "sufficient conditions"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 19,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}