{
  "id": "1305.0722",
  "version": "v1",
  "published": "2013-05-03T14:29:05.000Z",
  "updated": "2013-05-03T14:29:05.000Z",
  "title": "A note on the series representation for the density of the supremum of a stable process",
  "authors": [
    "Daniel Hackmann",
    "Alexey Kuznetsov"
  ],
  "comment": "6 pages",
  "categories": [
    "math.PR"
  ],
  "abstract": "An absolutely convergent double series representation for the density of the supremum of $\\alpha$-stable Levy process is given in [3, Theorem 2] for almost all irrational $\\alpha$. This result cannot be made stronger in the following sense: the series does not converge absolutely when $\\alpha$ belongs to a certain subset of irrational numbers of Lebesgue measure zero (see [6, Theorem 2]). Our main result in this note shows that for every irrational $\\alpha$ there is a way to rearrange the terms of the double series, so that it converges to the density of the supremum. We show how one can establish this stronger result by introducing a simple yet non-trivial modification in the original proof of [3,Theorem 2].",
  "revisions": [
    {
      "version": "v1",
      "updated": "2013-05-03T14:29:05.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "60G52"
    ],
    "keywords": [
      "stable process",
      "absolutely convergent double series representation",
      "irrational",
      "lebesgue measure zero",
      "stronger result"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 6,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2013arXiv1305.0722H"
    }
  }
}