{
  "id": "0905.3358",
  "version": "v1",
  "published": "2009-05-20T17:11:21.000Z",
  "updated": "2009-05-20T17:11:21.000Z",
  "title": "Path regularity of Gaussian processes via small deviations",
  "authors": [
    "Frank Aurzada"
  ],
  "comment": "19pages",
  "categories": [
    "math.PR"
  ],
  "abstract": "We study the a.s. sample path regularity of Gaussian processes. To this end we relate the path regularity directly to the theory of small deviations. In particular, we show that if the process is $n$-times differentiable then the exponential rate of decay of its small deviations is at most $\\varepsilon^{-1/n}$. We also show a similar result if $n$ is not an integer.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2009-05-20T17:11:21.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "60G15",
      "60F99"
    ],
    "keywords": [
      "small deviations",
      "gaussian processes",
      "sample path regularity",
      "exponential rate",
      "similar result"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 19,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2009arXiv0905.3358A"
    }
  }
}