Essec\Faculty\Model\Contribution {#2233
  #_index: "academ_contributions"
  #_id: "9872"
  #_source: array:26 [
    "id" => "9872"
    "slug" => "chaos-expansions-and-level-crossings"
    "yearMonth" => "2000-09"
    "year" => "2000"
    "title" => "Chaos expansions and level crossings"
    "description" => "KRATZ, M. (2000). <i>Chaos expansions and level crossings</i>."
    "authors" => array:1 [
      0 => array:3 [
        "name" => "KRATZ Marie"
        "bid" => "B00072305"
        "slug" => "kratz-marie"
      ]
    ]
    "ouvrage" => ""
    "keywords" => []
    "updatedAt" => "2021-07-13 14:31:22"
    "publicationUrl" => null
    "publicationInfo" => array:3 [
      "pages" => null
      "volume" => null
      "number" => null
    ]
    "type" => array:2 [
      "fr" => "Documents de travail"
      "en" => "Working Papers"
    ]
    "support_type" => array:2 [
      "fr" => null
      "en" => null
    ]
    "countries" => array:2 [
      "fr" => null
      "en" => null
    ]
    "abstract" => array:2 [
      "fr" => """
        In this paper we show that the number of crossings at any \n
        level by a smooth stationary Gaussian process X on the interval [0,t] can be defined as $N_t(x)= \int_0^t \delta_x(X_s)\n
        | \dot X_s| ds$ in the Sobolev space D(2,alpha) for any alpha <1/4.
        """
      "en" => """
        In this paper we show that the number of crossings at any \n
        level by a smooth stationary Gaussian process X on the interval [0,t] can be defined as $N_t(x)= \int_0^t \delta_x(X_s)\n
        | \dot X_s| ds$ in the Sobolev space D(2,alpha) for any alpha <1/4.
        """
    ]
    "authors_fields" => array:2 [
      "fr" => "Systèmes d'Information, Data Analytics et Opérations"
      "en" => "Information Systems, Data Analytics and Operations"
    ]
    "indexedAt" => "2024-12-21T14:21:48.000Z"
    "docTitle" => "Chaos expansions and level crossings"
    "docSurtitle" => "Documents de travail"
    "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">Systèmes d'Information, Data Analytics et Opérations</span> | <span class="document-property-year">2000</span>"
    "keywordList" => ""
    "docPreview" => "<b>Chaos expansions and level crossings</b><br><span>2000-09 | Documents de travail </span>"
    "docType" => "research"
    "publicationLink" => "<a href="#" target="_blank">Chaos expansions and level crossings</a>"
  ]
  +lang: "fr"
  +"_type": "_doc"
  +"_score": 9.039552
  +"parent": null
}