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Essec\Faculty\Model\Contribution {#2216 ▼
  #_index: "academ_contributions"
  #_id: "1905"
  #_source: array:26 [
    "id" => "1905"
    "slug" => "1905-level-crossings-and-other-level-functionals-of-stationary-gaussian-processes"
    "yearMonth" => "2006-01"
    "year" => "2006"
    "title" => "Level Crossings and Other Level Functionals of Stationary Gaussian Processes"
    "description" => "KRATZ, M. (2006). Level Crossings and Other Level Functionals of Stationary Gaussian Processes. <i>Probability Surveys</i>, pp. 230-288. KRATZ, M. (2006). Level Crossings and Other Level Functionals of Stationary Gaussian Processes. <i>P "
    "authors" => array:1 [
      0 => array:3 [
        "name" => "KRATZ Marie"
        "bid" => "B00072305"
        "slug" => "kratz-marie"
      ]
    ]
    "ouvrage" => ""
    "keywords" => array:2 [
      0 => "Gaussian processes"
      1 => "Hermite polynomials"
    ]
    "updatedAt" => "2020-12-17 17:55:06"
    "publicationUrl" => null
    "publicationInfo" => array:3 [
      "pages" => "230-288"
      "volume" => null
      "number" => null
    ]
    "type" => array:2 [
      "fr" => "Articles"
      "en" => "Journal articles"
    ]
    "support_type" => array:2 [
      "fr" => "Revue scientifique"
      "en" => "Scientific journal"
    ]
    "countries" => array:2 [
      "fr" => null
      "en" => null
    ]
    "abstract" => array:2 [
      "fr" => "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. This paper presents a synthesis on the mathematical work done on level crossings of stationary Gauss "
      "en" => "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. This paper presents a synthesis on the mathematical work done on level crossings of stationary Gauss "
    ]
    "authors_fields" => array:2 [
      "fr" => "Systèmes d'Information, Data Analytics et Opérations"
      "en" => "Information Systems, Data Analytics and Operations"
    ]
    "indexedAt" => "2025-03-20T23:21:41.000Z"
    "docTitle" => "Level Crossings and Other Level Functionals of Stationary Gaussian Processes"
    "docSurtitle" => "Journal articles"
    "authorNames" => "<a href="/cv/kratz-marie">KRATZ Marie</a>"
    "docDescription" => "<span class="document-property-authors">KRATZ Marie</span><br><span class="document-property-authors_fields">Information Systems, Data Analytics and Operations</span> | <span class="document-property-year">2006</span> <span class="document-property-authors">KRATZ Marie</span><br><span class="document-property-authors "
    "keywordList" => "<a href="#">Gaussian processes</a>, <a href="#">Hermite polynomials</a>"
    "docPreview" => "<b>Level Crossings and Other Level Functionals of Stationary Gaussian Processes</b><br><span>2006-01 | Journal articles </span> <b>Level Crossings and Other Level Functionals of Stationary Gaussian Processes</b><br><span>2006-01 "
    "docType" => "research"
    "publicationLink" => "<a href="#" target="_blank">Level Crossings and Other Level Functionals of Stationary Gaussian Processes</a> <a href="#" target="_blank">Level Crossings and Other Level Functionals of Stationary Gaussian Proce "
  ]
  +lang: "en"
  +"_type": "_doc"
  +"_score": 9.159047
  +"parent": null
}