{
  "id": "1710.08130",
  "version": "v1",
  "published": "2017-10-23T07:59:54.000Z",
  "updated": "2017-10-23T07:59:54.000Z",
  "title": "A semigroup approach to nonlinear Lévy processes",
  "authors": [
    "Robert Denk",
    "Michael Kupper",
    "Max Nendel"
  ],
  "comment": "22 pages",
  "categories": [
    "math.PR"
  ],
  "abstract": "We study the relation between L\\'evy processes under nonlinear expectations, nonlinear semigroups and fully nonlinear PDEs. First, we establish a one-to-one relation between nonlinear L\\'evy processes and nonlinear Markovian convolution semigroups. Second, we provide a condition on a family of infinitesimal generators $(A_\\lambda)_{\\lambda\\in\\Lambda}$ of linear L\\'evy processes which guarantees the existence of a nonlinear L\\'evy processes such that the corresponding nonlinear Markovian convolution semigroup is a viscosity solution of the fully nonlinear PDE $\\partial_t u=\\sup_{\\lambda\\in \\Lambda} A_\\lambda u$. The results are illustrated with several examples.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2017-10-23T07:59:54.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "60G51",
      "49L25",
      "47H20"
    ],
    "keywords": [
      "nonlinear lévy processes",
      "semigroup approach",
      "nonlinear levy processes",
      "fully nonlinear pde",
      "corresponding nonlinear markovian convolution semigroup"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 22,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}