{
  "id": "1005.3766",
  "version": "v1",
  "published": "2010-05-20T17:35:11.000Z",
  "updated": "2010-05-20T17:35:11.000Z",
  "title": "Uniqueness in Law for the Allen-Cahn SPDE via Change of Measure",
  "authors": [
    "Hassan Allouba"
  ],
  "comment": "6 pages, 1/9 papers of my 2000-2006 collection (preprint version)",
  "journal": "C. R. Acad. Sci. Paris S\\'er. I Math. 330 (2000), no. 5, 371-376",
  "doi": "10.1016/S0764-4442(00)00190-7",
  "categories": [
    "math.PR",
    "math-ph",
    "math.AP",
    "math.MP"
  ],
  "abstract": "We start by first using change of measure to prove the transfer of uniqueness in law among pairs of parabolic SPDEs differing only by a drift function, under an almost sure $L^2$ condition on the drift/diffusion ratio. This is a considerably weaker condition than the usual Novikov one, and it allows us to prove uniqueness in law for the Allen-Cahn SPDE driven by space-time white noise with diffusion function $a(t,x,u)=Cu^\\gamma$, $1/2\\le\\gamma\\le1$ and $C\\ne0$. The same transfer result is also valid for ordinary SDEs and hyperbolic SPDEs.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2010-05-20T17:35:11.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "60H15",
      "35A02"
    ],
    "keywords": [
      "uniqueness",
      "space-time white noise",
      "allen-cahn spde driven",
      "diffusion function",
      "parabolic spdes"
    ],
    "tags": [
      "journal article"
    ],
    "publication": {
      "journal": "Academie des Sciences Paris Comptes Rendus Serie Sciences Mathematiques",
      "year": 2000,
      "month": "Mar",
      "volume": 330,
      "number": 5,
      "pages": 371
    },
    "note": {
      "typesetting": "TeX",
      "pages": 6,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2000CRASM.330..371A"
    }
  }
}