{
  "id": "1503.05532",
  "version": "v1",
  "published": "2015-03-18T19:02:38.000Z",
  "updated": "2015-03-18T19:02:38.000Z",
  "title": "On the functional CLT for stationary Markov Chains started at a point",
  "authors": [
    "David Barrera",
    "Costel Peligrad",
    "Magda Peligrad"
  ],
  "comment": "Dedicated to the memory of Mikhail Gordin, 20 pages",
  "categories": [
    "math.PR"
  ],
  "abstract": "We present a general functional central limit theorem started at a point also known under the name of quenched. As a consequence, we point out several new classes of stationary processes, defined via projection conditions, which satisfy this type of asymptotic result. One of the theorems shows that if a Markov chain is stationary ergodic and reversible, this result holds for bounded additive functionals of the chain which have a martingale coboundary in L_1 representation. Our results are also well adapted for strongly mixing sequences providing for this case an alternative, shorter approach to some recent results in the literature.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2015-03-18T19:02:38.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "60G10",
      "60G42",
      "60J05"
    ],
    "keywords": [
      "stationary markov chains",
      "functional clt",
      "general functional central limit theorem"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 20,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2015arXiv150305532B"
    }
  }
}