{
  "id": "math/0602381",
  "version": "v1",
  "published": "2006-02-17T16:27:19.000Z",
  "updated": "2006-02-17T16:27:19.000Z",
  "title": "Distortion mismatch in the quantization of probability measures",
  "authors": [
    "Siegried Graf",
    "Harald Luschgy",
    "Gilles Pagès"
  ],
  "comment": "25p",
  "categories": [
    "math.PR"
  ],
  "abstract": "We elucidate the asymptotics of the L^s-quantization error induced by a sequence of L^r-optimal n-quantizers of a probability distribution P on R^d when s>r. In particular we show that under natural assumptions, the optimal rate is preserved as long as s<r+d (and for every s in the case of a compactly supported distribution). We derive some applications of these results to the error bounds for quantization based quadrature formulae in numerical integration on R^d and on the Wiener space.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2006-02-17T16:27:19.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "60G15",
      "60G35",
      "41A25"
    ],
    "keywords": [
      "probability measures",
      "distortion mismatch",
      "quantization",
      "wiener space",
      "quadrature formulae"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2006math......2381G"
    }
  }
}