{
  "id": "math/0612577",
  "version": "v1",
  "published": "2006-12-20T07:05:41.000Z",
  "updated": "2006-12-20T07:05:41.000Z",
  "title": "Level crossings and other level functionals of stationary Gaussian processes",
  "authors": [
    "Marie F. Kratz"
  ],
  "comment": "Published at http://dx.doi.org/10.1214/154957806000000087 in the Probability Surveys (http://www.i-journals.org/ps/) by the Institute of Mathematical Statistics (http://www.imstat.org)",
  "journal": "Probability Surveys 2006, Vol. 3, 230-288",
  "doi": "10.1214/154957806000000087",
  "categories": [
    "math.PR"
  ],
  "abstract": "This paper presents a synthesis on the mathematical work done on level crossings of stationary Gaussian processes, with some extensions. The main results [(factorial) moments, representation into the Wiener Chaos, asymptotic results, rate of convergence, local time and number of crossings] are described, as well as the different approaches [normal comparison method, Rice method, Stein-Chen method, a general $m$-dependent method] used to obtain them; these methods are also very useful in the general context of Gaussian fields. Finally some extensions [time occupation functionals, number of maxima in an interval, process indexed by a bidimensional set] are proposed, illustrating the generality of the methods. A large inventory of papers and books on the subject ends the survey.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2006-12-20T07:05:41.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "60G15",
      "60G10",
      "60G12",
      "60G60",
      "60G70",
      "60F05"
    ],
    "keywords": [
      "stationary gaussian processes",
      "level crossings",
      "level functionals",
      "time occupation functionals",
      "normal comparison method"
    ],
    "tags": [
      "journal article"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2006math.....12577K"
    }
  }
}