{
  "id": "1203.5695",
  "version": "v1",
  "published": "2012-03-26T15:08:39.000Z",
  "updated": "2012-03-26T15:08:39.000Z",
  "title": "Estimates for the rate of strong approximation in Hilbert space",
  "authors": [
    "Friedrich Götze",
    "Andrei Yu. Zaitsev"
  ],
  "comment": "15 pages",
  "journal": "published in Siberian Mathematical Journal, 2011, v. 52, no. 4, 796-808",
  "categories": [
    "math.PR"
  ],
  "abstract": "The aim of this paper is to investigate, which infinite dimensional consequences follow from the main results of recently published paper of the authors (2009) (see Theorems 2 and 3). We show that the finite dimensional Theorem 3 implies meaningful estimates for the rate of strong Gaussian approximation of sums of i.i.d. Hilbert space valued random vectors $\\xi_j$ with finite moments $E |\\xi_j|^\\gamma$, $\\gamma>2$. We show that the rate of approximation depends substantially on the rate of decay of the sequence of eigenvalues of the covariance operator of summands.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2012-03-26T15:08:39.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "60F05"
    ],
    "keywords": [
      "strong approximation",
      "hilbert space valued random vectors",
      "strong gaussian approximation",
      "finite dimensional theorem",
      "infinite dimensional consequences"
    ],
    "tags": [
      "journal article"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 15,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2012arXiv1203.5695G"
    }
  }
}