{
  "id": "1410.4643",
  "version": "v1",
  "published": "2014-10-17T06:06:09.000Z",
  "updated": "2014-10-17T06:06:09.000Z",
  "title": "Local times in a Brownian excursion",
  "authors": [
    "Krishna B. Athreya",
    "Raoul Normand",
    "Vivekananda Roy",
    "Sheng-Jhih Wu"
  ],
  "comment": "8 pages",
  "categories": [
    "math.PR"
  ],
  "abstract": "Let $\\{B(t), t \\geq 0\\}$ be a standard Brownian motion in $\\mathbb{R}$. Let $T$ be the first return time to 0 after hitting 1, and $\\{L(T,x), x \\in \\mathbb{R}\\}$ be the local time process at time $T$ and level $x$. The distribution of $L(T,x)$ for each $x \\in \\mathbb{R}$ is determined. This is applied to the estimation of a $L^1$ integral on $\\mathbb{R}$.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2014-10-17T06:06:09.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "60J65",
      "60F05"
    ],
    "keywords": [
      "brownian excursion",
      "standard brownian motion",
      "local time process",
      "first return time",
      "distribution"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 8,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2014arXiv1410.4643A"
    }
  }
}