{
  "id": "1302.4419",
  "version": "v3",
  "published": "2013-02-18T20:38:49.000Z",
  "updated": "2013-02-27T07:15:57.000Z",
  "title": "The determinant of the Malliavin matrix and the determinant of the covariance matrix for multiple integrals",
  "authors": [
    "Ciprian Tudor"
  ],
  "comment": "Shortly after the publication of the first version of the paper on arxiv, we realized that the there is a mistake in one of the proofs. The formula for the determinant of the Malliavin matrix was correct but the relations (19) and (20) in the first version were wrong (or not yet proven)",
  "categories": [
    "math.PR"
  ],
  "abstract": "A well-known problem in Malliavin calculus concerns the relation between the determinant of the Malliavin matrix of a random vector and the determinant of its covariance matrix. We give an explicit relation between these two determinants for couples of random vectors of multiple integrals. In particular, if the multiple integrals are of the same order and this order is at most 4, we prove that two random variables in the same Wiener chaos either admit a joint density, either are proportional and that the result is not true for random variables in Wiener chaoses of different orders.",
  "revisions": [
    {
      "version": "v3",
      "updated": "2013-02-27T07:15:57.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "multiple integrals",
      "determinant",
      "malliavin matrix",
      "covariance matrix",
      "random variables"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2013arXiv1302.4419T"
    }
  }
}