{
  "id": "1606.08208",
  "version": "v1",
  "published": "2016-06-27T11:06:19.000Z",
  "updated": "2016-06-27T11:06:19.000Z",
  "title": "The winding of stationary Gaussian processes",
  "authors": [
    "Jeremiah Buckley",
    "Naomi Feldheim"
  ],
  "comment": "27 pages",
  "categories": [
    "math.PR",
    "math.CA",
    "math.CV"
  ],
  "abstract": "This paper studies the winding of a continuously differentiable Gaussian stationary process $f:\\mathbb{R}\\to\\mathbb{C}$ in the interval $[0,T]$. We give formulae for the mean and the variance of this random variable. The variance is shown to always grow at least linearly with $T$, and conditions for it to be asymptotically linear or quadratic are given. Moreover, we show that if the covariance function together with its second derivative are in $L^2(\\mathbb{R})$, then the winding obeys a central limit theorem. These results correspond to similar results for zeroes of real-valued stationary Gaussian functions by Cuzick, Slud and others.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2016-06-27T11:06:19.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "60G15",
      "60G10",
      "30E99"
    ],
    "keywords": [
      "stationary gaussian processes",
      "central limit theorem",
      "real-valued stationary gaussian functions",
      "continuously differentiable gaussian stationary process",
      "results correspond"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 27,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}