{
  "id": "1307.7559",
  "version": "v7",
  "published": "2013-07-29T12:44:03.000Z",
  "updated": "2016-01-06T11:27:35.000Z",
  "title": "Integral representation of random variables with respect to Gaussian processes",
  "authors": [
    "Lauri Viitasaari"
  ],
  "comment": "Published at http://dx.doi.org/10.3150/14-BEJ662 in the Bernoulli (http://isi.cbs.nl/bernoulli/) by the International Statistical Institute/Bernoulli Society (http://isi.cbs.nl/BS/bshome.htm)",
  "journal": "Bernoulli 2016, Vol. 22, No. 1, 376-395",
  "doi": "10.3150/14-BEJ662",
  "categories": [
    "math.PR"
  ],
  "abstract": "It was shown in Mishura et al. (Stochastic Process. Appl. 123 (2013) 2353-2369), that any random variable can be represented as improper pathwise integral with respect to fractional Brownian motion. In this paper, we extend this result to cover a wide class of Gaussian processes. In particular, we consider a wide class of processes that are H\\\"{o}lder continuous of order $\\alpha>1/2$ and show that only local properties of the covariance function play role for such results.",
  "revisions": [
    {
      "version": "v6",
      "updated": "2014-01-13T12:08:24.000Z",
      "abstract": "It was shown in \\cite{m-s-v} that any random variable can be represented as improper pathwise integral with respect to fractional Brownian motion. In this paper we extend this result to cover a wide class of Gaussian processes. In particular, we consider a wide class of processes that are H\\\"{o}lder continuous of order $\\alpha>{1}{2}$ and show that only local properties of the covariance function play role for such results.",
      "comment": "17 pages",
      "journal": null,
      "doi": null
    },
    {
      "version": "v7",
      "updated": "2016-01-06T11:27:35.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "60H05",
      "60G15"
    ],
    "keywords": [
      "gaussian processes",
      "random variable",
      "integral representation",
      "wide class",
      "covariance function play role"
    ],
    "tags": [
      "journal article"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 17,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2013arXiv1307.7559V"
    }
  }
}