{
  "id": "1208.1908",
  "version": "v1",
  "published": "2012-08-09T13:44:34.000Z",
  "updated": "2012-08-09T13:44:34.000Z",
  "title": "CLT for an iterated integral with respect to fBm with H > 1/2",
  "authors": [
    "Daniel Harnett",
    "David Nualart"
  ],
  "doi": "10.1080/17442508.2013.774403",
  "categories": [
    "math.PR"
  ],
  "abstract": "We construct an iterated stochastic integral with fractional Brownian motion with H > 1/2. The first integrand is a deterministic function, and each successive integral is with respect to an independent fBm. We show that this symmetric stochastic integral is equal to the Malliavin divergence integral. By a version of the Fourth Moment theorem of Nualart and Peccati, we show that a family of such integrals converges in distribution to a scaled Brownian motion. An application is an approximation to the windings for a planar fBm, previously studied by Baudoin and Nualart.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2012-08-09T13:44:34.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "60F05",
      "60H05",
      "60H07"
    ],
    "keywords": [
      "iterated integral",
      "symmetric stochastic integral",
      "fourth moment theorem",
      "malliavin divergence integral",
      "fractional brownian motion"
    ],
    "tags": [
      "journal article"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2012arXiv1208.1908H"
    }
  }
}