Essec\Faculty\Model\Contribution {#2190`
#_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" => "2024-04-21T07:21:51.000Z"
"docTitle" => "Multilevel Particle Filters for the Non-Linear Filtering Problem in Continuous Time"
"docSurtitle" => "Journal 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">Information Systems, Decision Sciences and Statistics</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 | Journal 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: "en"
+"_type": "_doc"
+"_score": 8.910406
+"parent": null
}