{
  "id": "2003.09281",
  "version": "v1",
  "published": "2020-03-20T14:03:03.000Z",
  "updated": "2020-03-20T14:03:03.000Z",
  "title": "Non-asymptotic control of the cumulative distribution function of Lévy processes",
  "authors": [
    "Céline Duval",
    "Ester Mariucci"
  ],
  "categories": [
    "math.PR",
    "math.ST",
    "stat.TH"
  ],
  "abstract": "We propose non-asymptotic controls of the cumulative distribution function $P(|X_{t}|\\ge \\varepsilon)$, for any $t>0$, $\\varepsilon>0$ and any L\\'evy process $X$ such that its L\\'evy density is bounded from above by the density of an $\\alpha$-stable type L\\'evy process in a neighborhood of the origin. The results presented are non-asymptotic and optimal, they apply to a large class of L\\'evy processes.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2020-03-20T14:03:03.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "cumulative distribution function",
      "non-asymptotic control",
      "lévy processes",
      "stable type levy process",
      "large class"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}