{
  "id": "1010.3603",
  "version": "v2",
  "published": "2010-10-18T14:07:47.000Z",
  "updated": "2012-01-27T17:06:36.000Z",
  "title": "A convergent series representation for the density of the supremum of a stable process",
  "authors": [
    "Friedrich Hubalek",
    "Alexey Kuznetsov"
  ],
  "comment": "12 pages",
  "journal": "Electron. Commun. Probab., 16, no. 8, 84-95, 2011",
  "doi": "10.1214/ECP.v16-1601",
  "categories": [
    "math.PR"
  ],
  "abstract": "We study the density of the supremum of a strictly stable L\\'evy process. We prove that for almost all values of the index $\\alpha$ -- except for a dense set of Lebesgue measure zero -- the asymptotic series which were obtained in A. Kuznetsov (2010) \"On extrema of stable processes\" are in fact absolutely convergent series representations for the density of the supremum.",
  "revisions": [
    {
      "version": "v2",
      "updated": "2012-01-27T17:06:36.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "60G52"
    ],
    "keywords": [
      "stable process",
      "fact absolutely convergent series representations",
      "lebesgue measure zero",
      "strictly stable levy process",
      "asymptotic series"
    ],
    "tags": [
      "journal article"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 12,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2010arXiv1010.3603H"
    }
  }
}