{
  "id": "1109.0838",
  "version": "v2",
  "published": "2011-09-05T09:30:48.000Z",
  "updated": "2012-07-11T06:05:27.000Z",
  "title": "A central limit theorem for stationary random fields",
  "authors": [
    "Mohamed El Machkouri",
    "Dalibor Volny",
    "Wei Biao Wu"
  ],
  "comment": "22 pages",
  "categories": [
    "math.PR",
    "math.ST",
    "stat.TH"
  ],
  "abstract": "This paper establishes a central limit theorem and an invariance principle for a wide class of stationary random fields under natural and easily verifiable conditions. More precisely, we deal with random fields of the form $X_k = g(\\varepsilon_{k-s}, s \\in \\Z^d)$, $k\\in\\Z^d$, where $(\\varepsilon_i)_{i\\in\\Z^d}$ are i.i.d random variables and $g$ is a measurable function. Such kind of spatial processes provides a general framework for stationary ergodic random fields. Under a short-range dependence condition, we show that the central limit theorem holds without any assumption on the underlying domain on which the process is observed. A limit theorem for the sample auto-covariance function is also established.",
  "revisions": [
    {
      "version": "v2",
      "updated": "2012-07-11T06:05:27.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "stationary random fields",
      "stationary ergodic random fields",
      "central limit theorem holds",
      "sample auto-covariance function",
      "short-range dependence condition"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 22,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2011arXiv1109.0838E"
    }
  }
}