Essec\Faculty\Model\Contribution {#2220
  #_index: "academ_contributions"
  #_id: "16041"
  #_source: array:26 [
    "id" => 16041
    "slug" => "16041-solving-the-poisson-equation-using-coupled-markov-chains"
    "yearMonth" => "2026-02"
    "year" => 2026
    "title" => "Solving the Poisson equation using coupled Markov chains"
    "description" => "DOUC, R., JACOB, P., LEE, A. et VATS, D. (2026). Solving the Poisson equation using coupled Markov chains. <i>Annals of Statistics</i>, 54(1), pp. 201-225."
    "authors" => array:4 [
      0 => array:3 [
        "name" => "JACOB Pierre"
        "bid" => "B00795650"
        "slug" => "jacob-pierre"
      ]
      1 => array:1 [
        "name" => "DOUC Randal"
      ]
      2 => array:1 [
        "name" => "LEE Anthony"
      ]
      3 => array:1 [
        "name" => "VATS Dootika"
      ]
    ]
    "ouvrage" => ""
    "keywords" => array:3 [
      0 => "Unbiased estimation"
      1 => "Coupled Markov chains"
      2 => "Poisson equation solutions"
    ]
    "updatedAt" => "2026-04-01 09:12:14"
    "publicationUrl" => "https://doi.org/10.1214/25-AOS2564"
    "publicationInfo" => array:3 [
      "pages" => "201-225"
      "volume" => "54"
      "number" => "1"
    ]
    "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" => "This article shows how coupled Markov chains that meet exactly after a random number of iterations can be used to generate unbiased estimators of the solutions of the Poisson equation. Through this connection, we re-derive known unbiased estimators of expectations with respect to the stationary distribution of a Markov chain and provide conditions for the finiteness of their moments. We further construct unbiased estimators of the asymptotic variance of Markov chain ergodic averages, and provide conditions for the finiteness of the estimators' moments of any order. If their second moment is finite, the average of independent copies of such estimators converges to the asymptotic variance at the Monte Carlo rate, comparing favorably to known rates for batch means and spectral variance estimators. The results are illustrated with numerical experiments."
      "en" => "This article shows how coupled Markov chains that meet exactly after a random number of iterations can be used to generate unbiased estimators of the solutions of the Poisson equation. Through this connection, we re-derive known unbiased estimators of expectations with respect to the stationary distribution of a Markov chain and provide conditions for the finiteness of their moments. We further construct unbiased estimators of the asymptotic variance of Markov chain ergodic averages, and provide conditions for the finiteness of the estimators' moments of any order. If their second moment is finite, the average of independent copies of such estimators converges to the asymptotic variance at the Monte Carlo rate, comparing favorably to known rates for batch means and spectral variance estimators. The results are illustrated with numerical experiments."
    ]
    "authors_fields" => array:2 [
      "fr" => "Systèmes d'Information, Data Analytics et Opérations"
      "en" => "Information Systems, Data Analytics and Operations"
    ]
    "indexedAt" => "2026-04-03T18:23:22.000Z"
    "docTitle" => "Solving the Poisson equation using coupled Markov chains"
    "docSurtitle" => "Journal articles"
    "authorNames" => "<a href="/cv/jacob-pierre">JACOB Pierre</a>, DOUC Randal, LEE Anthony, VATS Dootika"
    "docDescription" => "<span class="document-property-authors">JACOB Pierre, DOUC Randal, LEE Anthony, VATS Dootika</span><br><span class="document-property-authors_fields">Information Systems, Data Analytics and Operations</span> | <span class="document-property-year">2026</span>"
    "keywordList" => "<a href="#">Unbiased estimation</a>, <a href="#">Coupled Markov chains</a>, <a href="#">Poisson equation solutions</a>"
    "docPreview" => "<b>Solving the Poisson equation using coupled Markov chains</b><br><span>2026-02 | Journal articles </span>"
    "docType" => "research"
    "publicationLink" => "<a href="https://doi.org/10.1214/25-AOS2564" target="_blank">Solving the Poisson equation using coupled Markov chains</a>"
  ]
  +lang: "en"
  +"_score": 8.994999
  +"_ignored": array:2 [
    0 => "abstract.en.keyword"
    1 => "abstract.fr.keyword"
  ]
  +"parent": null
}