{
  "id": "0809.4560",
  "version": "v1",
  "published": "2008-09-26T08:35:39.000Z",
  "updated": "2008-09-26T08:35:39.000Z",
  "title": "Boundary non-crossings of Brownian pillow",
  "authors": [
    "Enkelejd Hashorva"
  ],
  "comment": "14 pages",
  "doi": "10.1007/s10959-008-0191-5",
  "categories": [
    "math.PR",
    "math.ST",
    "stat.TH"
  ],
  "abstract": "Let B_0(s,t) be a Brownian pillow with continuous sample paths, and let h,u:[0,1]^2\\to R be two measurable functions. In this paper we derive upper and lower bounds for the boundary non-crossing probability \\psi(u;h):=P{B_0(s,t)+h(s,t) \\le u(s,t), \\forall s,t\\in [0,1]}. Further we investigate the asymptotic behaviour of $\\psi(u;\\gamma h)$ with $\\gamma$ tending to infinity, and solve a related minimisation problem.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2008-09-26T08:35:39.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "60F10",
      "60G15"
    ],
    "keywords": [
      "brownian pillow",
      "related minimisation problem",
      "asymptotic behaviour",
      "lower bounds",
      "boundary non-crossing probability"
    ],
    "tags": [
      "journal article"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 14,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2008arXiv0809.4560H"
    }
  }
}