{
  "id": "1301.5715",
  "version": "v2",
  "published": "2013-01-24T07:04:55.000Z",
  "updated": "2013-08-01T18:41:51.000Z",
  "title": "The covariation for Banach space valued processes and applications",
  "authors": [
    "Cristina Di Girolami",
    "Giorgio Fabbri",
    "Francesco Russo"
  ],
  "categories": [
    "math.PR"
  ],
  "abstract": "This article focuses on a new concept of quadratic variation for processes taking values in a Banach space $B$ and a corresponding covariation. This is more general than the classical one of M\\'etivier and Pellaumail. Those notions are associated with some subspace $\\chi$ of the dual of the projective tensor product of $B$ with itself. We also introduce the notion of a convolution type process, which is a natural generalization of the It\\^o process and the concept of $\\bar \\nu_0$-semimartingale, which is a natural extension of the classical notion of semimartingale. The framework is the stochastic calculus via regularization in Banach spaces. Two main applications are mentioned: one related to Clark-Ocone formula for finite quadratic variation processes; the second one concerns the probabilistic representation of a Hilbert valued partial differential equation of Kolmogorov type.",
  "revisions": [
    {
      "version": "v2",
      "updated": "2013-08-01T18:41:51.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "banach space valued processes",
      "covariation",
      "applications",
      "hilbert valued partial differential equation",
      "finite quadratic variation processes"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2013arXiv1301.5715D"
    }
  }
}