{
  "id": "0801.2751",
  "version": "v3",
  "published": "2008-01-17T19:27:53.000Z",
  "updated": "2010-11-24T06:34:07.000Z",
  "title": "Construction of an Edwards' probability measure on $\\mathcal{C}(\\mathbb{R}_+,\\mathbb{R})$",
  "authors": [
    "Joseph Najnudel"
  ],
  "comment": "Published in at http://dx.doi.org/10.1214/10-AOP540 the Annals of Probability (http://www.imstat.org/aop/) by the Institute of Mathematical Statistics (http://www.imstat.org)",
  "journal": "Annals of Probability 2010, Vol. 38, No. 6, 2295-2321",
  "doi": "10.1214/10-AOP540",
  "categories": [
    "math.PR"
  ],
  "abstract": "In this article, we prove that the measures $\\mathbb{Q}_T$ associated to the one-dimensional Edwards' model on the interval $[0,T]$ converge to a limit measure $\\mathbb{Q}$ when $T$ goes to infinity, in the following sense: for all $s\\geq0$ and for all events $\\Lambda_s$ depending on the canonical process only up to time $s$, $\\mathbb{Q}_T(\\Lambda_s)\\rightarrow\\mathbb{Q}(\\Lambda_s)$. Moreover, we prove that, if $\\mathbb{P}$ is Wiener measure, there exists a martingale $(D_s)_{s\\in\\mathbb{R}_+}$ such that $\\mathbb{Q}(\\Lambda_s) =\\mathbb{E}_{\\mathbb{P}}(\\mathbh{1}_{\\Lambda_s}D_s)$, and we give an explicit expression for this martingale.",
  "revisions": [
    {
      "version": "v3",
      "updated": "2010-11-24T06:34:07.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "probability measure",
      "construction",
      "limit measure",
      "wiener measure",
      "martingale"
    ],
    "tags": [
      "journal article"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2008arXiv0801.2751N"
    }
  }
}