{
  "id": "1212.2383",
  "version": "v2",
  "published": "2012-12-11T11:00:06.000Z",
  "updated": "2013-11-22T14:33:41.000Z",
  "title": "Generalized dimensions of images of measures under Gaussian processes",
  "authors": [
    "Kenneth Falconer",
    "Yimin Xiao"
  ],
  "comment": "26 pages",
  "categories": [
    "math.PR"
  ],
  "abstract": "We show that for certain Gaussian random processes and fields X:R^N to R^d, D_q(mu_X) = min{d, D_q(mu)/alpha} a.s. for an index alpha which depends on Holder properties and strong local nondeterminism of X, where q>1, where D_q denotes generalized q-dimension and where mu_X is the image of the measure mu under X. In particular this holds for index-alpha fractional Brownian motion, for fractional Riesz-Bessel motions and for certain infinity scale fractional Brownian motions.",
  "revisions": [
    {
      "version": "v2",
      "updated": "2013-11-22T14:33:41.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "60G22",
      "28A80"
    ],
    "keywords": [
      "gaussian processes",
      "generalized dimensions",
      "infinity scale fractional brownian motions",
      "index-alpha fractional brownian motion",
      "gaussian random processes"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 26,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2012arXiv1212.2383F"
    }
  }
}