{
  "id": "1904.00595",
  "version": "v1",
  "published": "2019-04-01T07:00:50.000Z",
  "updated": "2019-04-01T07:00:50.000Z",
  "title": "Integral representations for the Hartman--Watson density",
  "authors": [
    "Yuu Hariya"
  ],
  "comment": "14 pages",
  "categories": [
    "math.PR"
  ],
  "abstract": "This paper concerns the density of the Hartman--Watson law. Yor (1980) obtained an integral formula that gives a closed-form expression of the Hartman--Watson density. In this paper, based on Yor's formula, we provide alternative integral representations for the density. As an immediate application, we recover in part a Dufresne's result (2001) that exhibits remarkably simple representations for densities of the laws of exponential additive functionals of Brownian motion.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2019-04-01T07:00:50.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "60J65",
      "60J55",
      "60E10"
    ],
    "keywords": [
      "hartman-watson density",
      "paper concerns",
      "brownian motion",
      "hartman-watson law",
      "integral formula"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 14,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}