{
  "id": "1601.05567",
  "version": "v1",
  "published": "2016-01-21T09:42:37.000Z",
  "updated": "2016-01-21T09:42:37.000Z",
  "title": "A deviation bound for $α$-dependent sequences with applications to intermittent maps",
  "authors": [
    "J Dedecker",
    "Florence Merlevède"
  ],
  "categories": [
    "math.PR"
  ],
  "abstract": "We prove a deviation bound for the maximum of partial sums of functions of $\\alpha$-dependent sequences as defined in Dedecker, Gou{\\\"e}zel and Merlev{\\`e}de (2010). As a consequence, we extend the Rosenthal inequality of Rio (2000) for $\\alpha$-mixing sequences in the sense of Rosenblatt (1956) to the larger class of $\\alpha$-dependent sequences. Starting from the deviation inequality, we obtain upper bounds for large deviations and an H{\\\"o}lderian invariance principle for the Donsker line. We illustrate our results through the example of intermittent maps of the interval, which are not $\\alpha$-mixing in the sense of Rosenblatt.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2016-01-21T09:42:37.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "dependent sequences",
      "intermittent maps",
      "deviation bound",
      "applications",
      "donsker line"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2016arXiv160105567D"
    }
  }
}