Essec\Faculty\Model\Contribution {#2233
  #_index: "academ_contributions"
  #_id: "10143"
  #_source: array:26 [
    "id" => "10143"
    "slug" => "on-the-second-moment-of-the-number-of-crossings-by-a-stationary-gaussian-process"
    "yearMonth" => "2006-07"
    "year" => "2006"
    "title" => "On the second moment of the number of crossings by a stationary Gaussian process"
    "description" => "KRATZ, M. et LEON, J. (2006). On the second moment of the number of crossings by a stationary Gaussian process. <i>Annals of Probability</i>, 34(4), pp. 1601-1607."
    "authors" => array:2 [
      0 => array:3 [
        "name" => "KRATZ Marie"
        "bid" => "B00072305"
        "slug" => "kratz-marie"
      ]
      1 => array:1 [
        "name" => "LEON José"
      ]
    ]
    "ouvrage" => ""
    "keywords" => array:4 [
      0 => """
        AMS classification -\n
        60G15 -60G10 -60G70Crossings
        """
      1 => "Gaussian processes"
      2 => "Geman condition"
      3 => "Hermite polynomials -level curve -spectral moment"
    ]
    "updatedAt" => "2021-07-13 14:31:27"
    "publicationUrl" => null
    "publicationInfo" => array:3 [
      "pages" => "1601-1607"
      "volume" => "34"
      "number" => "4"
    ]
    "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" => "Cramér and Leadbetter introduced a sufficient condition  to have a finite variance of the zeros number of a centered stationary Gaussian process with twice differentiable covariance function r. This condition is known as the Geman condition since Geman proved in 1972 that it was also a necessary condition. Up to now no such criterion was known for counts of crossings of a level other than the mean. This paper shows taht the Geman condition is still sufficient and necessary to have a finite variance of the number of any fixed level crossings. For the generalization to the number of a curve crossings, a condition on the curve has to be added to the Geman conditiion."
      "en" => "Cramér and Leadbetter introduced a sufficient condition  to have a finite variance of the zeros number of a centered stationary Gaussian process with twice differentiable covariance function r. This condition is known as the Geman condition since Geman proved in 1972 that it was also a necessary condition. Up to now no such criterion was known for counts of crossings of a level other than the mean. This paper shows taht the Geman condition is still sufficient and necessary to have a finite variance of the number of any fixed level crossings. For the generalization to the number of a curve crossings, a condition on the curve has to be added to the Geman conditiion."
    ]
    "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 second moment of the number of crossings by a stationary Gaussian process"
    "docSurtitle" => "Articles"
    "authorNames" => "<a href="/cv/kratz-marie">KRATZ Marie</a>, LEON José"
    "docDescription" => "<span class="document-property-authors">KRATZ Marie, LEON José</span><br><span class="document-property-authors_fields">Systèmes d'Information, Data Analytics et Opérations</span> | <span class="document-property-year">2006</span>"
    "keywordList" => """
      <a href="#">AMS classification -\n
      60G15 -60G10 -60G70Crossings</a>, <a href="#">Gaussian processes</a>, <a href="#">Geman condition</a>, <a href="#">Hermite polynomials -level curve -spectral moment</a>
      """
    "docPreview" => "<b>On the second moment of the number of crossings by a stationary Gaussian process</b><br><span>2006-07 | Articles </span>"
    "docType" => "research"
    "publicationLink" => "<a href="#" target="_blank">On the second moment of the number of crossings by a stationary Gaussian process</a>"
  ]
  +lang: "fr"
  +"_type": "_doc"
  +"_score": 8.677269
  +"parent": null
}