{
  "id": "math/0605433",
  "version": "v3",
  "published": "2006-05-16T12:30:11.000Z",
  "updated": "2006-11-01T14:44:16.000Z",
  "title": "Sufficient Conditions for the Invertibility of Adapted Perturbations of Identity on the Wiener Space",
  "authors": [
    "Ali Suleyman Ustunel",
    "Moshe Zakai"
  ],
  "categories": [
    "math.PR",
    "math.FA",
    "math.ST",
    "stat.TH"
  ],
  "abstract": "Let $(W,H,\\mu)$ be the classical Wiener space. Assume that $U=I_W+u$ is an adapted perturbation of identity, i.e., $u:W\\to H$ is adapted to the canonical filtration of $W$. We give some sufficient analytic conditions on $u$ which imply the invertibility of the map $U$. In particular it is shown that if $u\\in \\DD_{p,1}(H)$ is adapted and if $\\exp({1/2}\\|\\nabla u\\|_2^2-\\delta u)\\in L^q(\\mu)$, where $p^{-1}+q^{-1}=1$, then $I_W+u$ is almost surely invertible. As a consequence, if, there exists an integer $k\\geq 1$ such that $\\|\\nabla^k u\\|_{H^{\\otimes(k+1)}}\\in L^\\infty(\\mu)$, then $I_W+u$ is again almost surely invertible.",
  "revisions": [
    {
      "version": "v3",
      "updated": "2006-11-01T14:44:16.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "60H07",
      "60H05",
      "60H25",
      "60G15",
      "60G30",
      "60G35",
      "46G12",
      "47H05",
      "35J60"
    ],
    "keywords": [
      "adapted perturbation",
      "sufficient conditions",
      "invertibility",
      "sufficient analytic conditions",
      "classical wiener space"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2006math......5433S"
    }
  }
}