{
  "id": "1401.7253",
  "version": "v2",
  "published": "2014-01-28T16:50:58.000Z",
  "updated": "2015-01-11T19:19:37.000Z",
  "title": "Nonlinear Lévy Processes and their Characteristics",
  "authors": [
    "Ariel Neufeld",
    "Marcel Nutz"
  ],
  "comment": "36 pages; forthcoming in 'Transactions of the American Mathematical Society'",
  "categories": [
    "math.PR",
    "math.AP",
    "math.OC"
  ],
  "abstract": "We develop a general construction for nonlinear L\\'evy processes with given characteristics. More precisely, given a set $\\Theta$ of L\\'evy triplets, we construct a sublinear expectation on Skorohod space under which the canonical process has stationary independent increments and a nonlinear generator corresponding to the supremum of all generators of classical L\\'evy processes with triplets in $\\Theta$. The nonlinear L\\'evy process yields a tractable model for Knightian uncertainty about the distribution of jumps for which expectations of Markovian functionals can be calculated by means of a partial integro-differential equation.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2014-01-28T16:50:58.000Z",
      "comment": "35 pages",
      "journal": null,
      "doi": null
    },
    {
      "version": "v2",
      "updated": "2015-01-11T19:19:37.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "60G51",
      "60G44",
      "93E20"
    ],
    "keywords": [
      "nonlinear lévy processes",
      "characteristics",
      "nonlinear levy process yields",
      "partial integro-differential equation",
      "stationary independent increments"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 36,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2014arXiv1401.7253N"
    }
  }
}