{
  "id": "1103.0935",
  "version": "v3",
  "published": "2011-03-04T16:04:18.000Z",
  "updated": "2013-07-08T08:49:17.000Z",
  "title": "Suprema of Lévy processes",
  "authors": [
    "Mateusz Kwaśnicki",
    "Jacek Małecki",
    "Michał Ryznar"
  ],
  "comment": "Published in at http://dx.doi.org/10.1214/11-AOP719 the Annals of Probability (http://www.imstat.org/aop/) by the Institute of Mathematical Statistics (http://www.imstat.org)",
  "journal": "Annals of Probability 2013, Vol. 41, No. 3B, 2047-2065",
  "doi": "10.1214/11-AOP719",
  "categories": [
    "math.PR"
  ],
  "abstract": "In this paper we study the supremum functional $M_t=\\sup_{0\\le s\\le t}X_s$, where $X_t$, $t\\ge0$, is a one-dimensional L\\'{e}vy process. Under very mild assumptions we provide a simple, uniform estimate of the cumulative distribution function of $M_t$. In the symmetric case we find an integral representation of the Laplace transform of the distribution of $M_t$ if the L\\'{e}vy-Khintchin exponent of the process increases on $(0,\\infty)$.",
  "revisions": [
    {
      "version": "v3",
      "updated": "2013-07-08T08:49:17.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "lévy processes",
      "uniform estimate",
      "supremum functional",
      "cumulative distribution function",
      "mild assumptions"
    ],
    "tags": [
      "journal article"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2011arXiv1103.0935K"
    }
  }
}