{
  "id": "2111.13206",
  "version": "v2",
  "published": "2021-11-25T18:23:20.000Z",
  "updated": "2022-08-09T17:33:16.000Z",
  "title": "Length of stationary Gaussian excursions",
  "authors": [
    "Arijit Chakrabarty",
    "Manish Pandey",
    "Sukrit Chakraborty"
  ],
  "comment": "To appear in the Proceedings of the American Mathematical Society",
  "categories": [
    "math.PR"
  ],
  "abstract": "Given that a stationary Gaussian process is above a high threshold, the length of time it spends before going below that threshold is studied. The asymptotic order is determined by the smoothness of the sample paths, which in turn is a function of the tails of the spectral measure. Two disjoint regimes are studied - one in which the second spectral moment is finite and the other in which the tails of the spectral measure are regularly varying and the second moment is infinite.",
  "revisions": [
    {
      "version": "v2",
      "updated": "2022-08-09T17:33:16.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "stationary gaussian excursions",
      "spectral measure",
      "second spectral moment",
      "stationary gaussian process",
      "second moment"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}