{
  "id": "1206.5415",
  "version": "v2",
  "published": "2012-06-23T17:10:11.000Z",
  "updated": "2015-03-06T11:51:06.000Z",
  "title": "On fractional smoothness and $L_p$-approximation on the Gaussian space",
  "authors": [
    "Stefan Geiss",
    "Anni Toivola"
  ],
  "comment": "Published in at http://dx.doi.org/10.1214/13-AOP884 the Annals of Probability (http://www.imstat.org/aop/) by the Institute of Mathematical Statistics (http://www.imstat.org)",
  "journal": "Annals of Probability 2015, Vol. 43, No. 2, 605-638",
  "doi": "10.1214/13-AOP884",
  "categories": [
    "math.PR"
  ],
  "abstract": "We consider Gaussian Besov spaces obtained by real interpolation and Riemann-Liouville operators of fractional integration on the Gaussian space and relate the fractional smoothness of a functional to the regularity of its heat extension. The results are applied to study an approximation problem in $L_p$ for $2\\le p<\\infty$ for stochastic integrals with respect to the $d$-dimensional (geometric) Brownian motion.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2012-06-23T17:10:11.000Z",
      "title": "On fractional smoothness and $L_p$-approximation on the Wiener space",
      "abstract": "We consider stochastic integral representations of $g(Y_1)$ with respect to a process $Y$, where $Y$ is the $d$-dimensional Brownian motion or the coordinate-wise geometric Brownian motion. For $2\\le p < \\infty$, we relate the $L_p$-norm of the discretization error of Riemann approximations of this integral to the Besov regularity of $g(Y_1)$ in the Malliavin sense and to the $L_p$-integrability of a Riemann-Liouville type operator.",
      "comment": null,
      "journal": null,
      "doi": null
    },
    {
      "version": "v2",
      "updated": "2015-03-06T11:51:06.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "60H05",
      "60H07",
      "41A25",
      "46B70"
    ],
    "keywords": [
      "wiener space",
      "fractional smoothness",
      "stochastic integral representations",
      "coordinate-wise geometric brownian motion",
      "riemann-liouville type operator"
    ],
    "tags": [
      "journal article"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2012arXiv1206.5415G"
    }
  }
}