{
  "id": "1404.0563",
  "version": "v1",
  "published": "2014-04-02T14:22:13.000Z",
  "updated": "2014-04-02T14:22:13.000Z",
  "title": "Moment bounds for dependent sequences in smooth Banach spaces",
  "authors": [
    "Jérôme Dedecker",
    "Florence Merlevède"
  ],
  "comment": "27 pages",
  "categories": [
    "math.PR"
  ],
  "abstract": "We prove a Marcinkiewicz-Zygmund type inequality for random variables taking values in a smooth Banach space. Next, we obtain some sharp concentration inequalities for the empirical measure of $\\{T, T^2, \\cdots, T^n\\}$, on a class of smooth functions, when $T$ belongs to a class of nonuniformly expanding maps of the unit interval.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2014-04-02T14:22:13.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "60E15",
      "60G48",
      "37E05"
    ],
    "keywords": [
      "smooth banach space",
      "dependent sequences",
      "moment bounds",
      "sharp concentration inequalities",
      "marcinkiewicz-zygmund type inequality"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 27,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2014arXiv1404.0563D"
    }
  }
}