Essec\Faculty\Model\Contribution {#2233
  #_index: "academ_contributions"
  #_id: "15106"
  #_source: array:26 [
    "id" => "15106"
    "slug" => "note-on-a-barbours-paper-on-steins-method-for-diffusion-approximations"
    "yearMonth" => "2017-04"
    "year" => "2017"
    "title" => "Note on A. Barbour’s paper on Stein’s method for diffusion approximations"
    "description" => "KASPRZAK, M., DUNCAN, A.B. et VOLLMER, S.J. (2017). Note on A. Barbour’s paper on Stein’s method for diffusion approximations. <i>Electronic Communications in Probability</i>, 22, pp. 1-8."
    "authors" => array:3 [
      0 => array:3 [
        "name" => "KASPRZAK Mikolaj"
        "bid" => "B00820408"
        "slug" => "kasprzak-mikolaj"
      ]
      1 => array:1 [
        "name" => "Duncan Andrew B."
      ]
      2 => array:1 [
        "name" => "Vollmer Sebastian J."
      ]
    ]
    "ouvrage" => ""
    "keywords" => array:3 [
      0 => "diffusion approximations"
      1 => "Donsker’s theorem"
      2 => "Stein’s method"
    ]
    "updatedAt" => "2024-10-31 13:51:19"
    "publicationUrl" => "https://doi.org/10.1214/17-ECP54"
    "publicationInfo" => array:3 [
      "pages" => "1-8"
      "volume" => "22"
      "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" => """
        In [2] foundations for diffusion approximation via Stein’s method are laid. This paper has been cited more than 130 times and is a cornerstone in the area of Stein’s method (see, for example, its use in [1] or [7]). A semigroup argument is used in [2] to solve a Stein equation for Gaussian diffusion approximation. We prove that, contrary to the claim in [2], the semigroup considered therein is not strongly continuous on the Banach space of continuous, real-valued functions on \n
        D\n
        [\n
        0\n
        ,\n
        1\n
        ]\n
         growing slower than a cubic, equipped with an appropriate norm. We also provide a proof of the exact formulation of the solution to the Stein equation of interest, which does not require the aforementioned strong continuity. This shows that the main results of [2] hold true.
        """
      "en" => """
        In [2] foundations for diffusion approximation via Stein’s method are laid. This paper has been cited more than 130 times and is a cornerstone in the area of Stein’s method (see, for example, its use in [1] or [7]). A semigroup argument is used in [2] to solve a Stein equation for Gaussian diffusion approximation. We prove that, contrary to the claim in [2], the semigroup considered therein is not strongly continuous on the Banach space of continuous, real-valued functions on \n
        D\n
        [\n
        0\n
        ,\n
        1\n
        ]\n
         growing slower than a cubic, equipped with an appropriate norm. We also provide a proof of the exact formulation of the solution to the Stein equation of interest, which does not require the aforementioned strong continuity. This shows that the main results of [2] hold true.
        """
    ]
    "authors_fields" => array:2 [
      "fr" => "Systèmes d'Information, Data Analytics et Opérations"
      "en" => "Information Systems, Data Analytics and Operations"
    ]
    "indexedAt" => "2024-11-23T09:21:42.000Z"
    "docTitle" => "Note on A. Barbour’s paper on Stein’s method for diffusion approximations"
    "docSurtitle" => "Articles"
    "authorNames" => "<a href="/cv/kasprzak-mikolaj">KASPRZAK Mikolaj</a>, Duncan Andrew B., Vollmer Sebastian J."
    "docDescription" => "<span class="document-property-authors">KASPRZAK Mikolaj, Duncan Andrew B., Vollmer Sebastian J.</span><br><span class="document-property-authors_fields">Systèmes d'Information, Data Analytics et Opérations</span> | <span class="document-property-year">2017</span>"
    "keywordList" => "<a href="#">diffusion approximations</a>, <a href="#">Donsker’s theorem</a>, <a href="#">Stein’s method</a>"
    "docPreview" => "<b>Note on A. Barbour’s paper on Stein’s method for diffusion approximations</b><br><span>2017-04 | Articles </span>"
    "docType" => "research"
    "publicationLink" => "<a href="https://doi.org/10.1214/17-ECP54" target="_blank">Note on A. Barbour’s paper on Stein’s method for diffusion approximations</a>"
  ]
  +lang: "fr"
  +"_type": "_doc"
  +"_score": 8.836839
  +"parent": null
}