{
  "id": "2105.15060",
  "version": "v1",
  "published": "2021-05-31T15:46:44.000Z",
  "updated": "2021-05-31T15:46:44.000Z",
  "title": "Convex minorants and the fluctuation theory of Lévy processes",
  "authors": [
    "Jorge Ignacio González Cázares",
    "Aleksandar Mijatović"
  ],
  "comment": "15 pages, 2 figures, short video on https://youtu.be/hEg4YmxOgXA",
  "categories": [
    "math.PR"
  ],
  "abstract": "We establish a novel characterisation of the law of the convex minorant of any L\\'evy process. Our self-contained elementary proof is based on the analysis of piecewise linear convex functions and requires only very basic properties of L\\'evy processes. Our main result provides a new simple and self-contained approach to the fluctuation theory of L\\'evy processes, circumventing local time and excursion theory. Easy corollaries include classical theorems, such as Rogozin's regularity criterion, Spitzer's identities and the Wiener-Hopf factorisation, as well as a novel factorisation identity.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2021-05-31T15:46:44.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "60G51"
    ],
    "keywords": [
      "convex minorant",
      "fluctuation theory",
      "lévy processes",
      "levy process",
      "novel factorisation identity"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 15,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}