Essec\Faculty\Model\Contribution {#2233
  #_index: "academ_contributions"
  #_id: "2129"
  #_source: array:26 [
    "id" => "2129"
    "slug" => "on-the-capacity-functional-of-excursion-sets-of-gaussian-random-fields-on-r%c2%b2"
    "yearMonth" => "2016-09"
    "year" => "2016"
    "title" => "On the Capacity Functional of Excursion Sets of Gaussian Random Fields on R²"
    "description" => "KRATZ, M. et NAGEL, W. (2016). On the Capacity Functional of Excursion Sets of Gaussian Random Fields on R². <i>Advances in Applied Probability</i>, 48(3), pp. 712-725."
    "authors" => array:2 [
      0 => array:3 [
        "name" => "KRATZ Marie"
        "bid" => "B00072305"
        "slug" => "kratz-marie"
      ]
      1 => array:1 [
        "name" => "NAGEL W."
      ]
    ]
    "ouvrage" => ""
    "keywords" => array:10 [
      0 => "Capacity functional"
      1 => "Crossings"
      2 => "Excursion set"
      3 => "Gaussian field"
      4 => "Growing circle method"
      5 => "Rice formula"
      6 => "Second moment measure"
      7 => "Sweeping line method"
      8 => "Stereology"
      9 => "Stochastic geometry"
    ]
    "updatedAt" => "2021-09-24 10:33:27"
    "publicationUrl" => "https://www.cambridge.org/core/journals/advances-in-applied-probability/article/abs/on-the-capacity-functional-of-excursion-sets-of-gaussian-random-fields-on-2/3A82FDC50E850497837BA1457551B43E"
    "publicationInfo" => array:3 [
      "pages" => "712-725"
      "volume" => "48"
      "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" => "When a random field (X_t, t in R²) is thresholded on a given level u, the excursion set is given by its indicator 1(X_t>u). The purpose of this work is to study functionals (as established in stochastic geometry) of these random excursion sets, as, e.g., the capacity functional as well as the second moment measure of the boundary length. It extends results obtained for the one-dimensional case to the two-dimensional case, with tools borrowed from crossings theory, in particular Rice methods, and from integral and stochastic geometry."
      "en" => "When a random field (X_t, t in R²) is thresholded on a given level u, the excursion set is given by its indicator 1(X_t>u). The purpose of this work is to study functionals (as established in stochastic geometry) of these random excursion sets, as, e.g., the capacity functional as well as the second moment measure of the boundary length. It extends results obtained for the one-dimensional case to the two-dimensional case, with tools borrowed from crossings theory, in particular Rice methods, and from integral and stochastic geometry."
    ]
    "authors_fields" => array:2 [
      "fr" => "Systèmes d'Information, Data Analytics et Opérations"
      "en" => "Information Systems, Data Analytics and Operations"
    ]
    "indexedAt" => "2024-12-21T13:21:43.000Z"
    "docTitle" => "On the Capacity Functional of Excursion Sets of Gaussian Random Fields on R²"
    "docSurtitle" => "Articles"
    "authorNames" => "<a href="/cv/kratz-marie">KRATZ Marie</a>, NAGEL W."
    "docDescription" => "<span class="document-property-authors">KRATZ Marie, NAGEL W.</span><br><span class="document-property-authors_fields">Systèmes d'Information, Data Analytics et Opérations</span> | <span class="document-property-year">2016</span>"
    "keywordList" => "<a href="#">Capacity functional</a>, <a href="#">Crossings</a>, <a href="#">Excursion set</a>, <a href="#">Gaussian field</a>, <a href="#">Growing circle method</a>, <a href="#">Rice formula</a>, <a href="#">Second moment measure</a>, <a href="#">Sweeping line method</a>, <a href="#">Stereology</a>, <a href="#">Stochastic geometry</a>"
    "docPreview" => "<b>On the Capacity Functional of Excursion Sets of Gaussian Random Fields on R²</b><br><span>2016-09 | Articles </span>"
    "docType" => "research"
    "publicationLink" => "<a href="https://www.cambridge.org/core/journals/advances-in-applied-probability/article/abs/on-the-capacity-functional-of-excursion-sets-of-gaussian-random-fields-on-2/3A82FDC50E850497837BA1457551B43E" target="_blank">On the Capacity Functional of Excursion Sets of Gaussian Random Fields on R²</a>"
  ]
  +lang: "fr"
  +"_type": "_doc"
  +"_score": 8.340796
  +"parent": null
}