{
  "id": "math/0312037",
  "version": "v2",
  "published": "2003-12-01T18:30:39.000Z",
  "updated": "2004-07-16T13:16:10.000Z",
  "title": "Sharp Integrability for Brownian Motion in Parabola-shaped Regions",
  "authors": [
    "Rodrigo Banuelos",
    "Tom Carroll"
  ],
  "categories": [
    "math.PR",
    "math.AP"
  ],
  "abstract": "We study the sharp order of integrability of the exit position of Brownian motion from the planar domains ${\\cal P}_\\alpha = \\{(x,y)\\in \\bR\\times \\bR\\colon x> 0, |y| < Ax^{\\alpha}\\}$, $0<\\alpha<1$. Together with some simple good-$\\lambda$ type arguments, this implies the order of integrability for the exit time of these domains; a result first proved for $\\alpha =1/2$ by Ba\\~nuelos, DeBlassie and Smits \\cite{ba} and for general $\\alpha$ by Li \\cite{li}. A sharp version of this result is also proved in higher dimensions.",
  "revisions": [
    {
      "version": "v2",
      "updated": "2004-07-16T13:16:10.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "brownian motion",
      "sharp integrability",
      "parabola-shaped regions",
      "sharp order",
      "higher dimensions"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2003math.....12037B"
    }
  }
}