{
  "id": "1109.5160",
  "version": "v3",
  "published": "2011-09-23T19:08:30.000Z",
  "updated": "2013-02-12T22:35:48.000Z",
  "title": "An invariance principle for fractional Brownian sheets",
  "authors": [
    "Yizao Wang"
  ],
  "comment": "Sections 1 and 5 revised. Accepted for publication in Journal of Theoretical Probability",
  "categories": [
    "math.PR"
  ],
  "abstract": "We establish a central limit theorem for partial sums of stationary linear random fields with dependent innovations, and an invariance principle for anisotropic fractional Brownian sheets. Our result is a generalization of the invariance principle for fractional Brownian motions by Dedecker et al. (2011) to high dimensions. A key ingredient of their argument, the martingale approximation, is replaced by an m-approximation argument. An important tool of our approach is a moment inequality for stationary random fields recently established by El Machkouri et al. (2011).",
  "revisions": [
    {
      "version": "v3",
      "updated": "2013-02-12T22:35:48.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "invariance principle",
      "anisotropic fractional brownian sheets",
      "stationary linear random fields",
      "central limit theorem",
      "fractional brownian motions"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2011arXiv1109.5160W"
    }
  }
}