{
  "id": "0809.0215",
  "version": "v1",
  "published": "2008-09-01T11:59:18.000Z",
  "updated": "2008-09-01T11:59:18.000Z",
  "title": "A necessary and sufficient condition for the invertibility of adapted perturbations of identity on the Wiener space",
  "authors": [
    "Ali Süleyman Üstünel"
  ],
  "journal": "Comptes Rendus Mathematiques, Vol. 346, 2008",
  "categories": [
    "math.PR",
    "math.FA"
  ],
  "abstract": "Let $(W,H,\\mu)$ be the classical Wiener space, assume that $U=I_W+u$ is an adapted perturbation of identity satisfying the Girsanov identity. Then, $U$ is invertible if and only if the kinetic energy of $u$ is equal to the relative entropy of the measure induced with the action of $U$ on the Wiener measure $\\mu$, in other words $U$ is invertible if and only if $$ \\half \\int_W|u|_H^2d\\mu=\\int_W \\frac{dU\\mu}{d\\mu}\\log\\frac{dU\\mu}{d\\mu}d\\mu . $$",
  "revisions": [
    {
      "version": "v1",
      "updated": "2008-09-01T11:59:18.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "60Hxx"
    ],
    "keywords": [
      "adapted perturbation",
      "sufficient condition",
      "invertibility",
      "classical wiener space",
      "girsanov identity"
    ],
    "tags": [
      "journal article"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2008arXiv0809.0215S"
    }
  }
}