Essec\Faculty\Model\Contribution {#6196
  #_index: "academ_contributions"
  #_id: "10950"
  #_source: array:26 [
    "id" => "10950"
    "slug" => "multilevel-particle-filters-for-the-non-linear-filtering-problem-in-continuous-time"
    "yearMonth" => "2020-06"
    "year" => "2020"
    "title" => "Multilevel Particle Filters for the Non-Linear Filtering Problem in Continuous Time"
    "description" => "HENG, J., YU, F. et HENG, J. (2020). Multilevel Particle Filters for the Non-Linear Filtering Problem in Continuous Time. <i>Statistics and Computing</i>, 30, pp. 1381-1402."
    "authors" => array:2 [
      0 => array:3 [
        "name" => "HENG Jeremy"
        "bid" => "B00760223"
        "slug" => "heng-jeremy"
      ]
      1 => array:1 [
        "name" => "YU F."
      ]
    ]
    "ouvrage" => ""
    "keywords" => array:3 [
      0 => "Multilevel Monte Carlo"
      1 => "Particle filters"
      2 => "Non-linear filtering"
    ]
    "updatedAt" => "2021-09-24 10:33:27"
    "publicationUrl" => "https://www.researchgate.net/publication/342253685_Multilevel_particle_filters_for_the_non-linear_filtering_problem_in_continuous_time"
    "publicationInfo" => array:3 [
      "pages" => "1381-1402"
      "volume" => "30"
      "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 the following article we consider the numerical approximation of the non-linear filter in continuous-time, where the observations and signal follow diffusion processes. Given access to high-frequency, but discrete-time observations, we resort to a first order time discretization of the non-linear filter, followed by an Euler discretization of the signal dynamics. In order to approximate the associated discretized non-linear filter, one can use a particle filter. Under assumptions, this can achieve a mean square error of \(\mathcal {O}(\epsilon ^2)\), for \(\epsilon >0\) arbitrary, such that the associated cost is \(\mathcal {O}(\epsilon ^{-4})\). We prove, under assumptions, that the multilevel particle filter of Jasra et al. (SIAM J Numer Anal 55:3068–3096, 2017) can achieve a mean square error of \(\mathcal {O}(\epsilon ^2)\), for cost \(\mathcal {O}(\epsilon ^{-3})\). This is supported by numerical simulations in several examples."
      "en" => "In the following article we consider the numerical approximation of the non-linear filter in continuous-time, where the observations and signal follow diffusion processes. Given access to high-frequency, but discrete-time observations, we resort to a first order time discretization of the non-linear filter, followed by an Euler discretization of the signal dynamics. In order to approximate the associated discretized non-linear filter, one can use a particle filter. Under assumptions, this can achieve a mean square error of \(\mathcal {O}(\epsilon ^2)\), for \(\epsilon >0\) arbitrary, such that the associated cost is \(\mathcal {O}(\epsilon ^{-4})\). We prove, under assumptions, that the multilevel particle filter of Jasra et al. (SIAM J Numer Anal 55:3068–3096, 2017) can achieve a mean square error of \(\mathcal {O}(\epsilon ^2)\), for cost \(\mathcal {O}(\epsilon ^{-3})\). This is supported by numerical simulations in several examples."
    ]
    "authors_fields" => array:2 [
      "fr" => "Systèmes d’Information, Sciences de la Décision et Statistiques"
      "en" => "Information Systems, Decision Sciences and Statistics"
    ]
    "indexedAt" => "2024-04-18T19:21:58.000Z"
    "docTitle" => "Multilevel Particle Filters for the Non-Linear Filtering Problem in Continuous Time"
    "docSurtitle" => "Articles"
    "authorNames" => "<a href="/cv/heng-jeremy">HENG Jeremy</a>, YU F."
    "docDescription" => "<span class="document-property-authors">HENG Jeremy, YU F.</span><br><span class="document-property-authors_fields">Systèmes d’Information, Sciences de la Décision et Statistiques</span> | <span class="document-property-year">2020</span>"
    "keywordList" => "<a href="#">Multilevel Monte Carlo</a>, <a href="#">Particle filters</a>, <a href="#">Non-linear filtering</a>"
    "docPreview" => "<b>Multilevel Particle Filters for the Non-Linear Filtering Problem in Continuous Time</b><br><span>2020-06 | Articles </span>"
    "docType" => "research"
    "publicationLink" => "<a href="https://www.researchgate.net/publication/342253685_Multilevel_particle_filters_for_the_non-linear_filtering_problem_in_continuous_time" target="_blank">Multilevel Particle Filters for the Non-Linear Filtering Problem in Continuous Time</a>"
  ]
  +lang: "fr"
  +"_type": "_doc"
  +"_score": 8.720232
  +"parent": null
}