{
  "id": "1602.05500",
  "version": "v1",
  "published": "2016-02-16T15:18:43.000Z",
  "updated": "2016-02-16T15:18:43.000Z",
  "title": "An Arctangent Law",
  "authors": [
    "Vassilis G. Papanicolaou"
  ],
  "comment": "3 pages",
  "categories": [
    "math.PR"
  ],
  "abstract": "Let $M_r$ be the maximum value of an one-dimensional Brownian motion on the (time) interval $[0, r]$. We derive an explicit formula for the distribution of the time required (after $r$) for the Brownian motion to exceed $M_r$.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2016-02-16T15:18:43.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "60J65"
    ],
    "keywords": [
      "arctangent law",
      "one-dimensional brownian motion",
      "explicit formula",
      "maximum value"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 3,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2016arXiv160205500P"
    }
  }
}