{
  "id": "0705.0135",
  "version": "v1",
  "published": "2007-05-01T16:30:48.000Z",
  "updated": "2007-05-01T16:30:48.000Z",
  "title": "Packing-Dimension Profiles and Fractional Brownian Motion",
  "authors": [
    "Davar Khoshnevisan",
    "Yimin Xiao"
  ],
  "categories": [
    "math.PR",
    "math.CA"
  ],
  "abstract": "In order to compute the packing dimension of orthogonal projections Falconer and Howroyd (1997) introduced a family of packing dimension profiles ${\\rm Dim}_s$ that are parametrized by real numbers $s>0$. Subsequently, Howroyd (2001) introduced alternate $s$-dimensional packing dimension profiles $\\hbox{${\\rm P}$-$\\dim$}_s$ and proved, among many other things, that $\\hbox{${\\rm P}$-$\\dim$}_s E={\\rm Dim}_s E$ for all integers $s>0$ and all analytic sets $E\\subseteq\\R^N$. The goal of this article is to prove that $\\hbox{${\\rm P}$-$\\dim$}_s E={\\rm Dim}_s E$ for all real numbers $s>0$ and analytic sets $E\\subseteq\\R^N$. This answers a question of Howroyd (2001, p. 159). Our proof hinges on a new property of fractional Brownian motion.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2007-05-01T16:30:48.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "60G15",
      "60G17",
      "28A80"
    ],
    "keywords": [
      "fractional brownian motion",
      "packing-dimension profiles",
      "analytic sets",
      "real numbers",
      "dimensional packing dimension profiles"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2007arXiv0705.0135K"
    }
  }
}