{
  "id": "0907.2501",
  "version": "v2",
  "published": "2009-07-15T06:44:55.000Z",
  "updated": "2009-08-22T09:26:17.000Z",
  "title": "On the structure of Gaussian random variables",
  "authors": [
    "Ciprian Tudor"
  ],
  "categories": [
    "math.PR"
  ],
  "abstract": "We study when a given Gaussian random variable on a given probability space $(\\Omega, {\\cal{F}}, P) $ is equal almost surely to $\\beta_{1}$ where $\\beta $ is a Brownian motion defined on the same (or possibly extended) probability space. As a consequences of this result, we prove that the distribution of a random variable (satisfying in addition a certain property) in a finite sum of Wiener chaoses cannot be normal. This result also allows to understand better some characterization of the Gaussian variables obtained via Malliavin calculus.",
  "revisions": [
    {
      "version": "v2",
      "updated": "2009-08-22T09:26:17.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "gaussian random variable",
      "probability space",
      "brownian motion",
      "malliavin calculus",
      "finite sum"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2009arXiv0907.2501T"
    }
  }
}