{
  "id": "math/0502057",
  "version": "v2",
  "published": "2005-02-02T20:52:22.000Z",
  "updated": "2005-02-02T21:02:41.000Z",
  "title": "A Sharp Inequality for Conditional Distribution of the First Exit Time of Brownian Motion",
  "authors": [
    "Majid Hosseini"
  ],
  "comment": "12 pages",
  "categories": [
    "math.PR"
  ],
  "abstract": "Let $U$ be a domain, convex in $x$ and symmetric about the y-axis, which is contained in a centered and oriented rectangle $R$. \\linebreak If $\\tau_A$ is the first exit time of Brownian motion from $A$ and $A^+=A\\cap \\{(x,y):x>0\\}$, it is proved that $P^z(\\tau_{U^+}>s\\mid \\tau_{R^+}>t)\\leq P^z(\\tau_{U}>s\\mid \\tau_{R}>t)$ for every $s,t>0$ and every $z\\in U^+$.",
  "revisions": [
    {
      "version": "v2",
      "updated": "2005-02-02T21:02:41.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "60J65",
      "60K99"
    ],
    "keywords": [
      "first exit time",
      "brownian motion",
      "conditional distribution",
      "sharp inequality",
      "oriented rectangle"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 12,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2005math......2057H"
    }
  }
}