{
  "id": "1210.3546",
  "version": "v2",
  "published": "2012-10-12T15:05:15.000Z",
  "updated": "2013-09-27T20:20:08.000Z",
  "title": "Empirical central limit theorems for ergodic automorphisms of the torus",
  "authors": [
    "J. Dedecker",
    "F. Merlevède",
    "F. Pène"
  ],
  "comment": "32 pages",
  "categories": [
    "math.PR"
  ],
  "abstract": "Let T be an ergodic automorphism of the d-dimensional torus T^d, and f be a continuous function from T^d to R^l. On the probability space T^d equipped with the Lebesgue-Haar measure, we prove the weak convergence of the sequential empirical process of the sequence (f o T^i)_{i \\geq 1} under some mild conditions on the modulus of continuity of f. The proofs are based on new limit theorems and new inequalities for non-adapted sequences, and on new estimates of the conditional expectations of f with respect to a natural filtration.",
  "revisions": [
    {
      "version": "v2",
      "updated": "2013-09-27T20:20:08.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "60F17",
      "37D30"
    ],
    "keywords": [
      "empirical central limit theorems",
      "ergodic automorphism",
      "probability space",
      "lebesgue-haar measure",
      "d-dimensional torus"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 32,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2012arXiv1210.3546D"
    }
  }
}