Essec\Faculty\Model\Contribution {#2205
  #_index: "academ_contributions"
  #_id: "1906"
  #_source: array:26 [
    "id" => "1906"
    "slug" => "level-curves-crossings-and-applications-for-gaussian-models"
    "yearMonth" => "2010-09"
    "year" => "2010"
    "title" => "Level Curves Crossings and Applications for Gaussian Models"
    "description" => "KRATZ, M. et LEON, J.R. (2010). Level Curves Crossings and Applications for Gaussian Models. <i>Extremes</i>, 13(3), pp. 315-351."
    "authors" => array:2 [
      0 => array:3 [
        "name" => "KRATZ Marie"
        "bid" => "B00072305"
        "slug" => "kratz-marie"
      ]
      1 => array:1 [
        "name" => "LEON J.R."
      ]
    ]
    "ouvrage" => ""
    "keywords" => array:9 [
      0 => "Co-area formula"
      1 => "Crossings"
      2 => "CLT"
      3 => "Gaussian fields"
      4 => "Harmonic oscillator"
      5 => "Hermite polynomials"
      6 => "Level curve"
      7 => "(Generalized) Rice formula"
      8 => "Specular point"
    ]
    "updatedAt" => "2021-02-02 16:16:18"
    "publicationUrl" => "https://link.springer.com/article/10.1007/s10687-009-0090-x"
    "publicationInfo" => array:3 [
      "pages" => "315-351"
      "volume" => "13"
      "number" => "3"
    ]
    "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" => "Representations into the Itô-Wiener Chaos and asymptotic results such as CLTs are obtained for the curve-crossings number of a stationary Gaussian process according to the form of the curve. Applications in physics and sea modelling follow, with the study of the estimator of the natural frequency of a harmonic oscillator and the study of specular points."
      "en" => "Representations into the Itô-Wiener Chaos and asymptotic results such as CLTs are obtained for the curve-crossings number of a stationary Gaussian process according to the form of the curve. Applications in physics and sea modelling follow, with the study of the estimator of the natural frequency of a harmonic oscillator and the study of specular points."
    ]
    "authors_fields" => array:2 [
      "fr" => "Systèmes d’Information, Sciences de la Décision et Statistiques"
      "en" => "Information Systems, Decision Sciences and Statistics"
    ]
    "indexedAt" => "2024-04-23T17:22:05.000Z"
    "docTitle" => "Level Curves Crossings and Applications for Gaussian Models"
    "docSurtitle" => "Articles"
    "authorNames" => "<a href="/cv/kratz-marie">KRATZ Marie</a>, LEON J.R."
    "docDescription" => "<span class="document-property-authors">KRATZ Marie, LEON J.R.</span><br><span class="document-property-authors_fields">Systèmes d’Information, Sciences de la Décision et Statistiques</span> | <span class="document-property-year">2010</span>"
    "keywordList" => "<a href="#">Co-area formula</a>, <a href="#">Crossings</a>, <a href="#">CLT</a>, <a href="#">Gaussian fields</a>, <a href="#">Harmonic oscillator</a>, <a href="#">Hermite polynomials</a>, <a href="#">Level curve</a>, <a href="#">(Generalized) Rice formula</a>, <a href="#">Specular point</a>"
    "docPreview" => "<b>Level Curves Crossings and Applications for Gaussian Models</b><br><span>2010-09 | Articles </span>"
    "docType" => "research"
    "publicationLink" => "<a href="https://link.springer.com/article/10.1007/s10687-009-0090-x" target="_blank">Level Curves Crossings and Applications for Gaussian Models</a>"
  ]
  +lang: "fr"
  +"_type": "_doc"
  +"_score": 9.167781
  +"parent": null
}