{
  "id": "1205.7022",
  "version": "v1",
  "published": "2012-05-31T15:43:24.000Z",
  "updated": "2012-05-31T15:43:24.000Z",
  "title": "Rates of convergence in the strong invariance principle for non adapted sequences. Application to ergodic automorphisms of the torus",
  "authors": [
    "J. Dedecker",
    "F. Merlevède",
    "F. Pène"
  ],
  "comment": "21 pages",
  "categories": [
    "math.PR"
  ],
  "abstract": "In this paper, we give rates of convergence in the strong invariance principle for non-adapted sequences satisfying projective criteria. The results apply to the iterates of ergodic automorphisms T of the d-dimensional torus, even in the non hyperbolic case. In this context, we give a large class of unbounded functions f from the d-dimensional torus to R, for which the partial sum foT+ foT^2 + ... + foT^n satisfies a strong invariance principle with an explicit rate of convergence.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2012-05-31T15:43:24.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "60F17",
      "37D30"
    ],
    "keywords": [
      "strong invariance principle",
      "non adapted sequences",
      "ergodic automorphisms",
      "convergence",
      "sequences satisfying projective criteria"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 21,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2012arXiv1205.7022D"
    }
  }
}