{
  "id": "math/0511545",
  "version": "v2",
  "published": "2005-11-22T09:20:18.000Z",
  "updated": "2006-05-16T14:03:57.000Z",
  "title": "The realization of positive random variables via absolutely continuous transformations of measure on Wiener space",
  "authors": [
    "D. Feyel",
    "A. S. Üstünel",
    "M. Zakai"
  ],
  "comment": "Published at http://dx.doi.org/10.1214/154957806000000069 in the Probability Surveys (http://www.i-journals.org/ps/) by the Institute of Mathematical Statistics (http://www.imstat.org)",
  "journal": "Probability Surveys 2006, Vol. 3, 170-205",
  "doi": "10.1214/154957806000000069",
  "categories": [
    "math.PR"
  ],
  "abstract": "Let $\\mu$ be a Gaussian measure on some measurable space $\\{W=\\{w\\},{\\mathcal{B}}(W)\\}$ and let $\\nu$ be a measure on the same space which is absolutely continuous with respect to $\\nu$. The paper surveys results on the problem of constructing a transformation $T$ on the $W$ space such that $Tw=w+u(w)$ where $u$ takes values in the Cameron-Martin space and the image of $\\mu$ under $T$ is $\\mu$. In addition we ask for the existence of transformations $T$ belonging to some particular classes.",
  "revisions": [
    {
      "version": "v2",
      "updated": "2006-05-16T14:03:57.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "positive random variables",
      "absolutely continuous transformations",
      "wiener space",
      "realization",
      "paper surveys results"
    ],
    "tags": [
      "journal article"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2005math.....11545F"
    }
  }
}