{
  "id": "1210.1560",
  "version": "v1",
  "published": "2012-10-04T19:42:59.000Z",
  "updated": "2012-10-04T19:42:59.000Z",
  "title": "Joint convergence along different subsequences of the signed cubic variation of fractional Brownian motion",
  "authors": [
    "Krzysztof Burdzy",
    "David Nualart",
    "Jason Swanson"
  ],
  "comment": "31 pages",
  "categories": [
    "math.PR"
  ],
  "abstract": "The purpose of this paper is to study the convergence in distribution of two subsequences of the signed cubic variation of the fractional Brownian motion with Hurst parameter $H=1/6$. We prove that, under some conditions on both subsequences, the limit is a two-dimensional Brownian motion whose components may be correlated and we find explicit formulae for its covariance function.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2012-10-04T19:42:59.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "60G22",
      "60F17"
    ],
    "keywords": [
      "fractional brownian motion",
      "signed cubic variation",
      "joint convergence",
      "subsequences",
      "two-dimensional brownian motion"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 31,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2012arXiv1210.1560B"
    }
  }
}