{
  "id": "math/0604211",
  "version": "v4",
  "published": "2006-04-10T00:49:44.000Z",
  "updated": "2006-12-05T11:18:35.000Z",
  "title": "The moment problem on the Wiener space",
  "authors": [
    "Frederik S Herzberg"
  ],
  "comment": "14 pages; Theorem 2 and Lemma 1 withdrawn",
  "categories": [
    "math.PR",
    "math.FA"
  ],
  "abstract": "Consider an $L^1$-continuous functional $\\ell$ on the vector space of polynomials of Brownian motion at given times, suppose $\\ell $ commutes with the quadratic variation in a natural sense, and consider a finite set of polynomials of Brownian motion at rational times, $f_1(\\vec b),...,f_m(\\vec b)$, mapping the Wiener space to $\\mathbb{R}$. In the spirit of Schm\\\"udgen's solution to the finite-dimensional moment problem, we give sufficient conditions under which $\\ell$ can be written in the form $\\int \\cdot d\\mu$ for some finite measure $\\mu$ on the Wiener space such that $\\mu$-almost surely, all the random variables $f_1(\\vec b),...,f_m(\\vec b)$ are nonnegative.",
  "revisions": [
    {
      "version": "v4",
      "updated": "2006-12-05T11:18:35.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "28C20",
      "28E05",
      "44A60",
      "03H05",
      "60J65"
    ],
    "keywords": [
      "wiener space",
      "brownian motion",
      "finite-dimensional moment problem",
      "sufficient conditions",
      "vector space"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 14,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2006math......4211H"
    }
  }
}