{
  "id": "0811.0909",
  "version": "v2",
  "published": "2008-11-06T10:08:41.000Z",
  "updated": "2008-12-18T13:24:45.000Z",
  "title": "Distribution of the Brownian motion on its way to hitting zero",
  "authors": [
    "P. Chigansky",
    "F. C. Klebaner"
  ],
  "comment": "7 pages, final version",
  "journal": "Elect. Comm. in Probab., 13(2008), pp. 641-648",
  "categories": [
    "math.PR",
    "math.ST",
    "stat.TH"
  ],
  "abstract": "For the one-dimensional Brownian motion $B=(B_t)_{t\\ge 0}$, started at $x>0$, and the first hitting time $\\tau=\\inf\\{t\\ge 0:B_t=0\\}$, we find the probability density of $B_{u\\tau}$ for a $u\\in(0,1)$, i.e. of the Brownian motion on its way to hitting zero.",
  "revisions": [
    {
      "version": "v2",
      "updated": "2008-12-18T13:24:45.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "60J65"
    ],
    "keywords": [
      "hitting zero",
      "distribution",
      "one-dimensional brownian motion",
      "probability density"
    ],
    "tags": [
      "journal article"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 7,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2008arXiv0811.0909C"
    }
  }
}