{
  "id": "0704.2826",
  "version": "v2",
  "published": "2007-04-21T21:13:44.000Z",
  "updated": "2008-08-28T12:55:33.000Z",
  "title": "Analytic crossing probabilities for certain barriers by Brownian motion",
  "authors": [
    "Nabil Kahale"
  ],
  "comment": "Published in at http://dx.doi.org/10.1214/07-AAP488 the Annals of Applied Probability (http://www.imstat.org/aap/) by the Institute of Mathematical Statistics (http://www.imstat.org)",
  "journal": "Annals of Applied Probability 2008, Vol. 18, No. 4, 1424-1440",
  "doi": "10.1214/07-AAP488",
  "categories": [
    "math.PR",
    "math.FA",
    "math.ST",
    "stat.TH"
  ],
  "abstract": "We calculate crossing probabilities and one-sided last exit time densities for a class of moving barriers on an interval $[0,T]$ via Schwartz distributions. We derive crossing probabilities and first hitting time densities for another class of barriers on $[0,T]$ by proving a Schwartz distribution version of the method of images. Analytic expressions for crossing probabilities and related densities are given for new explicit and semi-explicit barriers.",
  "revisions": [
    {
      "version": "v2",
      "updated": "2008-08-28T12:55:33.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "60J65",
      "60G40",
      "60J60"
    ],
    "keywords": [
      "analytic crossing probabilities",
      "brownian motion",
      "exit time densities",
      "schwartz distribution version",
      "first hitting time densities"
    ],
    "tags": [
      "journal article"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2007arXiv0704.2826K"
    }
  }
}