{
  "id": "1211.2973",
  "version": "v3",
  "published": "2012-11-13T12:46:41.000Z",
  "updated": "2014-11-10T19:20:43.000Z",
  "title": "Itô calculus and jump diffusions for $G$-Lévy processes",
  "authors": [
    "Krzysztof Paczka"
  ],
  "categories": [
    "math.PR"
  ],
  "abstract": "The paper considers the integration theory for $G$-L\\'evy processes with finite activity. We introduce the It\\^o-L\\'evy integrals, give the It\\^o formula for them and establish SDE's, BSDE's and decoupled FBSDE's driven by $G$-L\\'evy processes. In order to develop such a theory, we prove two key results: the representation of the sublinear expectation associated with a $G$-L\\'evy process and a characterization of random variables in $L^p_G(\\Omega)$ in terms of their quasi-continuity.",
  "revisions": [
    {
      "version": "v2",
      "updated": "2014-04-08T13:31:25.000Z",
      "comment": null,
      "journal": null,
      "doi": null
    },
    {
      "version": "v3",
      "updated": "2014-11-10T19:20:43.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "60H05",
      "60H10",
      "60G51"
    ],
    "keywords": [
      "lévy processes",
      "jump diffusions",
      "levy processes",
      "finite activity",
      "integration theory"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2012arXiv1211.2973P"
    }
  }
}