{
  "id": "0802.3112",
  "version": "v2",
  "published": "2008-02-21T13:53:18.000Z",
  "updated": "2010-11-10T10:00:42.000Z",
  "title": "Multiple Stratonovich integral and Hu--Meyer formula for Lévy processes",
  "authors": [
    "Mercè Farré",
    "Maria Jolis",
    "Frederic Utzet"
  ],
  "comment": "Published in at http://dx.doi.org/10.1214/10-AOP528 the Annals of Probability (http://www.imstat.org/aop/) by the Institute of Mathematical Statistics (http://www.imstat.org)",
  "journal": "Annals of Probability 2010, Vol. 38, No. 6, 2136-2169",
  "doi": "10.1214/10-AOP528",
  "categories": [
    "math.PR"
  ],
  "abstract": "In the framework of vector measures and the combinatorial approach to stochastic multiple integral introduced by Rota and Wallstrom [Ann. Probab. 25 (1997) 1257--1283], we present an It\\^{o} multiple integral and a Stratonovich multiple integral with respect to a L\\'{e}vy process with finite moments up to a convenient order. In such a framework, the Stratonovich multiple integral is an integral with respect to a product random measure whereas the It\\^{o} multiple integral corresponds to integrate with respect to a random measure that gives zero mass to the diagonal sets. A general Hu--Meyer formula that gives the relationship between both integrals is proved. As particular cases, the classical Hu--Meyer formulas for the Brownian motion and for the Poisson process are deduced. Furthermore, a pathwise interpretation for the multiple integrals with respect to a subordinator is given.",
  "revisions": [
    {
      "version": "v2",
      "updated": "2010-11-10T10:00:42.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "multiple stratonovich integral",
      "lévy processes",
      "stratonovich multiple integral",
      "stochastic multiple integral",
      "product random measure"
    ],
    "tags": [
      "journal article"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2008arXiv0802.3112F"
    }
  }
}