{
  "id": "math/0505026",
  "version": "v2",
  "published": "2005-05-02T16:46:21.000Z",
  "updated": "2005-10-07T19:10:15.000Z",
  "title": "Iterated Brownian motion in bounded domains in R^n",
  "authors": [
    "Erkan Nane"
  ],
  "comment": "17 pages",
  "journal": "Stochastic Processes and Their Applications, 116 (2006), 905-916.",
  "doi": "10.1016/j.spa.2005.10.007",
  "categories": [
    "math.PR"
  ],
  "abstract": "Let $\\tau_{D}(Z) $ is the first exit time of iterated Brownian motion from a domain $D \\subset \\RR{R}^{n}$ started at $z\\in D$ and let $P_{z}[\\tau_{D}(Z) >t]$ be its distribution. In this paper we establish the exact asymptotics of $P_{z}[\\tau_{D}(Z) >t]$ over bounded domains as an extension of the result in DeBlassie \\cite{deblassie}, for $z\\in D$ $$ P_{z}[\\tau_{D}(Z)>t]\\approx t^{1/2} \\exp(-{3/2}\\pi^{2/3}\\lambda_{D}^{2/3}t^{1/3}), as t\\to\\infty . $$ We also study asymptotics of the life time of Brownian-time Brownian motion (BTBM), $Z^{1}_{t}=z+X(Y(t))$, where $X_{t}$ and $Y_{t}$ are independent one-dimensional Brownian motions.",
  "revisions": [
    {
      "version": "v2",
      "updated": "2005-10-07T19:10:15.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "60J65",
      "60K99"
    ],
    "keywords": [
      "iterated brownian motion",
      "bounded domains",
      "independent one-dimensional brownian motions",
      "first exit time",
      "brownian-time brownian motion"
    ],
    "tags": [
      "journal article"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 17,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2005math......5026N"
    }
  }
}