{
  "id": "1007.2516",
  "version": "v1",
  "published": "2010-07-15T09:31:13.000Z",
  "updated": "2010-07-15T09:31:13.000Z",
  "title": "Lévy area for Gaussian processes: A double Wiener-Itô integral approach",
  "authors": [
    "Albert Ferreiro-Castilla",
    "Frederic Utzet"
  ],
  "categories": [
    "math.PR"
  ],
  "abstract": "Let $\\{X_{1}(t)\\}_{0\\leq t\\leq1}$ and $\\{X_{2}(t)\\}_{0\\leq t\\leq1}$ be two independent continuous centered Gaussian processes with covariance functions$R_{1}$ and $R_{2}$. This paper shows that if the covariance functions are of finite $p$-variation and $q$-variation respectively and such that $p^{-1}+q^{-1}>1$,then the L{\\'e}vy area can be defined as a double Wiener--It\\`o integral with respect to an isonormal Gaussian process induced by $X_{1}$ and $X_{2}$. Moreover, some properties of the characteristic function of that generalised L{\\'e}vy area are studied.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2010-07-15T09:31:13.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "integral approach",
      "lévy area",
      "covariance functions",
      "independent continuous centered gaussian processes",
      "isonormal gaussian process"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2010arXiv1007.2516F"
    }
  }
}