<?xml version="1.0" encoding="utf-8"?>
<TEI xmlns="http://www.tei-c.org/ns/1.0" xmlns:xsi="http://www.w3.org/2001/XMLSchema-instance" xmlns:hal="http://hal.archives-ouvertes.fr/" xmlns:gml="http://www.opengis.net/gml/3.3/" xmlns:gmlce="http://www.opengis.net/gml/3.3/ce" version="1.1" xsi:schemaLocation="http://www.tei-c.org/ns/1.0 http://api.archives-ouvertes.fr/documents/aofr-sword.xsd">
  <teiHeader>
    <fileDesc>
      <titleStmt>
        <title>HAL TEI export of inria-00550716</title>
      </titleStmt>
      <publicationStmt>
        <distributor>CCSD</distributor>
        <availability status="restricted">
          <licence target="https://creativecommons.org/publicdomain/zero/1.0/">CC0 1.0 - Universal</licence>
        </availability>
        <date when="2026-05-04T10:21:19+02:00"/>
      </publicationStmt>
      <sourceDesc>
        <p part="N">HAL API Platform</p>
      </sourceDesc>
    </fileDesc>
  </teiHeader>
  <text>
    <body>
      <listBibl>
        <biblFull>
          <titleStmt>
            <title xml:lang="en">Sampling per mode for rare event simulation in switching diffusions</title>
            <author role="aut">
              <persName>
                <forename type="first">Jaroslav</forename>
                <surname>Krystul</surname>
              </persName>
              <email type="md5">aef75e628aba3588da506b25d8af9558</email>
              <email type="domain">ewi.utwente.nl</email>
              <idno type="idhal" notation="numeric">885649</idno>
              <idno type="halauthorid" notation="string">518629-885649</idno>
              <orgName ref="#struct-303060"/>
              <affiliation ref="#struct-136621"/>
            </author>
            <author role="crp">
              <persName>
                <forename type="first">François</forename>
                <surname>Le Gland</surname>
              </persName>
              <email type="md5">8a88b982c8104240a806725914bdb16b</email>
              <email type="domain">inria.fr</email>
              <idno type="idhal" notation="numeric">832228</idno>
              <idno type="halauthorid" notation="string">129333-832228</idno>
              <orgName ref="#struct-300009"/>
              <affiliation ref="#struct-2511"/>
            </author>
            <author role="aut">
              <persName>
                <forename type="first">Pascal</forename>
                <surname>Lezaud</surname>
              </persName>
              <email type="md5">133f9bfa85aa0ade86060b093705e645</email>
              <email type="domain">recherche.enac.fr</email>
              <idno type="idhal" notation="string">pascal-lezaud</idno>
              <idno type="idhal" notation="numeric">7578</idno>
              <idno type="halauthorid" notation="string">21612-7578</idno>
              <idno type="IDREF">https://www.idref.fr/110417178</idno>
              <idno type="VIAF">https://viaf.org/viaf/200019202</idno>
              <idno type="ISNI">http://isni.org/isni/0000000431580378</idno>
              <orgName ref="#struct-380071"/>
              <affiliation ref="#struct-103280"/>
            </author>
            <editor role="depositor">
              <persName>
                <forename>Francois</forename>
                <surname>Le Gland</surname>
              </persName>
              <email type="md5">8a88b982c8104240a806725914bdb16b</email>
              <email type="domain">inria.fr</email>
            </editor>
            <funder ref="#projeurop-76104"/>
          </titleStmt>
          <editionStmt>
            <edition n="v1" type="current">
              <date type="whenSubmitted">2010-12-29 17:50:01</date>
              <date type="whenModified">2025-02-26 15:32:07</date>
              <date type="whenReleased">2010-12-29 18:08:31</date>
              <date type="whenProduced">2010-12-29</date>
              <date type="whenEndEmbargoed">2010-12-29</date>
              <ref type="file" target="https://inria.hal.science/inria-00550716v1/document">
                <date notBefore="2010-12-29"/>
              </ref>
              <ref type="file" subtype="author" n="1" target="https://inria.hal.science/inria-00550716v1/file/RR-7499.pdf" id="file-550716-1058523">
                <date notBefore="2010-12-29"/>
              </ref>
            </edition>
            <respStmt>
              <resp>contributor</resp>
              <name key="112617">
                <persName>
                  <forename>Francois</forename>
                  <surname>Le Gland</surname>
                </persName>
                <email type="md5">8a88b982c8104240a806725914bdb16b</email>
                <email type="domain">inria.fr</email>
              </name>
            </respStmt>
          </editionStmt>
          <publicationStmt>
            <distributor>CCSD</distributor>
            <idno type="halId">inria-00550716</idno>
            <idno type="halUri">https://inria.hal.science/inria-00550716</idno>
            <idno type="halBibtex">krystul:inria-00550716</idno>
            <idno type="halRefHtml">[Research Report] RR-7499, INRIA. 2010, pp.19</idno>
            <idno type="halRef">[Research Report] RR-7499, INRIA. 2010, pp.19</idno>
            <availability status="restricted">
              <licence target="https://about.hal.science/hal-authorisation-v1/">HAL Authorization<ref corresp="#file-550716-1058523"/></licence>
            </availability>
          </publicationStmt>
          <seriesStmt>
            <idno type="stamp" n="UNIV-RENNES1">Université de Rennes 1</idno>
            <idno type="stamp" n="IRMAR">Institut de Recherche Mathématique de Rennes</idno>
            <idno type="stamp" n="CNRS">CNRS - Centre national de la recherche scientifique</idno>
            <idno type="stamp" n="INRIA">INRIA - Institut National de Recherche en Informatique et en Automatique</idno>
            <idno type="stamp" n="INRIA-RENNES">INRIA Rennes - Bretagne Atlantique</idno>
            <idno type="stamp" n="IRISA">Irisa</idno>
            <idno type="stamp" n="INRIA-RRRT">Rapports de recherche et Technique de l'Inria</idno>
            <idno type="stamp" n="OPENAIRE">OpenAIRE</idno>
            <idno type="stamp" n="INRIA_TEST">INRIA - Institut National de Recherche en Informatique et en Automatique</idno>
            <idno type="stamp" n="TESTALAIN1">TESTALAIN1</idno>
            <idno type="stamp" n="IRMAR-PS">Processus stochastiques</idno>
            <idno type="stamp" n="IRISA-D5">SIGNAUX ET IMAGES NUMÉRIQUES, ROBOTIQUE</idno>
            <idno type="stamp" n="INRIA2">INRIA 2</idno>
            <idno type="stamp" n="UR1-HAL">Publications labos UR1 dans HAL-Rennes 1</idno>
            <idno type="stamp" n="LARA">LARA</idno>
            <idno type="stamp" n="UR1-MATH-STIC">UR1 - publications Maths-STIC</idno>
            <idno type="stamp" n="UR1-UFR-ISTIC">UFR ISTIC Informatique et électronique</idno>
            <idno type="stamp" n="DGAC">Direction Générale de l'Aviation Civile                     </idno>
            <idno type="stamp" n="TEST-UNIV-RENNES">TEST Université de Rennes</idno>
            <idno type="stamp" n="TEST-UR-CSS">TEST Université de Rennes CSS</idno>
            <idno type="stamp" n="UNIV-RENNES">Université de Rennes</idno>
            <idno type="stamp" n="INRIA-RENGRE">INRIA-RENGRE</idno>
            <idno type="stamp" n="INRIA-300009">Inria 300009</idno>
            <idno type="stamp" n="UR1-MATH-NUM">Pôle UnivRennes - Mathématiques - Numérique </idno>
          </seriesStmt>
          <notesStmt>
            <note type="audience" n="1">Not set</note>
            <note type="report" n="6">Research Report</note>
          </notesStmt>
          <sourceDesc>
            <biblStruct>
              <analytic>
                <title xml:lang="en">Sampling per mode for rare event simulation in switching diffusions</title>
                <author role="aut">
                  <persName>
                    <forename type="first">Jaroslav</forename>
                    <surname>Krystul</surname>
                  </persName>
                  <email type="md5">aef75e628aba3588da506b25d8af9558</email>
                  <email type="domain">ewi.utwente.nl</email>
                  <idno type="idhal" notation="numeric">885649</idno>
                  <idno type="halauthorid" notation="string">518629-885649</idno>
                  <orgName ref="#struct-303060"/>
                  <affiliation ref="#struct-136621"/>
                </author>
                <author role="crp">
                  <persName>
                    <forename type="first">François</forename>
                    <surname>Le Gland</surname>
                  </persName>
                  <email type="md5">8a88b982c8104240a806725914bdb16b</email>
                  <email type="domain">inria.fr</email>
                  <idno type="idhal" notation="numeric">832228</idno>
                  <idno type="halauthorid" notation="string">129333-832228</idno>
                  <orgName ref="#struct-300009"/>
                  <affiliation ref="#struct-2511"/>
                </author>
                <author role="aut">
                  <persName>
                    <forename type="first">Pascal</forename>
                    <surname>Lezaud</surname>
                  </persName>
                  <email type="md5">133f9bfa85aa0ade86060b093705e645</email>
                  <email type="domain">recherche.enac.fr</email>
                  <idno type="idhal" notation="string">pascal-lezaud</idno>
                  <idno type="idhal" notation="numeric">7578</idno>
                  <idno type="halauthorid" notation="string">21612-7578</idno>
                  <idno type="IDREF">https://www.idref.fr/110417178</idno>
                  <idno type="VIAF">https://viaf.org/viaf/200019202</idno>
                  <idno type="ISNI">http://isni.org/isni/0000000431580378</idno>
                  <orgName ref="#struct-380071"/>
                  <affiliation ref="#struct-103280"/>
                </author>
              </analytic>
              <monogr>
                <idno type="reportNumber">RR-7499</idno>
                <imprint>
                  <biblScope unit="pp">19</biblScope>
                  <date type="datePub">2010-12-29</date>
                </imprint>
                <authority type="institution">INRIA</authority>
              </monogr>
              <ref target="http://ifly.nlr.nl/" type="seeAlso"/>
            </biblStruct>
          </sourceDesc>
          <profileDesc>
            <langUsage>
              <language ident="en">English</language>
            </langUsage>
            <textClass>
              <keywords scheme="author">
                <term xml:lang="en">Rare event simulation</term>
                <term xml:lang="en">Switching diffusion</term>
                <term xml:lang="en">Multilevel splitting</term>
                <term xml:lang="en">Stratification</term>
                <term xml:lang="en">Central limit theorem (CLT)</term>
              </keywords>
              <classCode scheme="halDomain" n="math.math-pr">Mathematics [math]/Probability [math.PR]</classCode>
              <classCode scheme="halTypology" n="REPORT">Reports</classCode>
              <classCode scheme="halOldTypology" n="REPORT">Reports</classCode>
              <classCode scheme="halTreeTypology" n="REPORT.RESREPORT">Reports - Research report</classCode>
            </textClass>
            <abstract xml:lang="en">
              <p>An interacting particle system (IPS) approach is virtually applicable to estimate rare event for switching diffusions, since these processes own the strong Markov property. Nevertheless, in practice the straightforward application of this approach to switching diffusions fails to produce reasonable estimates within a reasonable amount of simulation time. This happens because each resampling step tends to sample more "heavy" particles from modes with higher probabilities, thus "light" particles in the modes with small probability tend to be discarded. To avoid this, a conditional "sampling per mode" algorithm has been proposed by Krystul (2006): instead of starting the algorithm with particles randomly distributed, we draw in each mode a fixed number of particles and at each resampling step, the same number of particles is sampled for each visited mode. In this paper, we establish a law of large numbers theorem as well as a central limit theorem (CLT) for the estimate of the rare event probability.</p>
            </abstract>
            <abstract xml:lang="fr">
              <p>Un algorithme de branchement multi-niveaux peut en principe être utilisé pour estimer des évènements rares dans des diffusions à paramètre markovien, puisque ces processus vérifient la propriété de Markov forte. En pratique, l'application directe de cet algorithme peut échouer à produire une estimation raisonnable en un temps de simulation raisonnable. En effet, chaque étape de ré-échantillonnage tend à favoriser les particules dans les modes de forte probabilité, de sorte que les particules dans les modes de faible probabilité tendent à être éliminées. Pour éviter cet écueil, un algorithme de ré-échantillonnage par mode a été proposé par Krystul (2006) : au lieu de démarrer l'algorithme avec des particules distribuées aléatoirement, on génère dans chaque mode un nombre fixé de particules, et à chaque étape de ré-échantillonnage, le même nombre de particules est généré dans chaque mode visité. Dans cet article, on établit une loi des grands nombres et un théorème central limite (TCL) pour l'estimation de la probabilité de l'évènement rare.</p>
            </abstract>
          </profileDesc>
        </biblFull>
      </listBibl>
    </body>
    <back>
      <listOrg type="structures">
        <org type="laboratory" xml:id="struct-136621" status="VALID">
          <orgName>Department of Applied Mathematics [Twente]</orgName>
          <desc>
            <address>
              <addrLine>PO Box 217 7500 AE Enschede The Netherlands</addrLine>
              <country key="NL"/>
            </address>
            <ref type="url">http://www.math.utwente.nl/research/index_eng.htm</ref>
          </desc>
          <listRelation>
            <relation active="#struct-303060" type="direct"/>
          </listRelation>
        </org>
        <org type="researchteam" xml:id="struct-2511" status="OLD">
          <idno type="RNSR">200518358M</idno>
          <orgName>Applications of interacting particle systems to statistics</orgName>
          <orgName type="acronym">ASPI</orgName>
          <date type="end">2012</date>
          <desc>
            <address>
              <addrLine>Campus de Beaulieu 35042 Rennes cedex</addrLine>
              <country key="FR"/>
            </address>
            <ref type="url">http://www.inria.fr/equipes/aspi</ref>
          </desc>
          <listRelation>
            <relation active="#struct-105160" type="direct"/>
            <relation active="#struct-419153" type="direct"/>
            <relation active="#struct-300009" type="indirect"/>
            <relation name="UMR6074" active="#struct-441569" type="direct"/>
          </listRelation>
        </org>
        <org type="department" xml:id="struct-103280" status="VALID">
          <orgName>Direction de la technique et de l'innovation de la DGAC</orgName>
          <orgName type="acronym">DTI</orgName>
          <date type="start">2005-03-01</date>
          <desc>
            <address>
              <country key="FR"/>
            </address>
          </desc>
          <listRelation>
            <relation active="#struct-302845" type="direct"/>
          </listRelation>
        </org>
        <org type="institution" xml:id="struct-303060" status="VALID">
          <idno type="ROR">https://ror.org/006hf6230</idno>
          <orgName>University of Twente</orgName>
          <desc>
            <address>
              <addrLine>Drienerlolaan 5, 7522 NB Enschede</addrLine>
              <country key="NL"/>
            </address>
            <ref type="url">https://www.utwente.nl/</ref>
          </desc>
        </org>
        <org type="institution" xml:id="struct-105160" status="VALID">
          <idno type="IdRef">26693823X</idno>
          <idno type="ROR">https://ror.org/015m7wh34</idno>
          <orgName>Université de Rennes</orgName>
          <orgName type="acronym">UR</orgName>
          <desc>
            <address>
              <addrLine>Campus de Beaulieu, 263 avenue Général Leclerc, CS 74205, 35042 RENNES CEDEX</addrLine>
              <country key="FR"/>
            </address>
            <ref type="url">https://www.univ-rennes.fr/</ref>
          </desc>
        </org>
        <org type="laboratory" xml:id="struct-419153" status="VALID">
          <idno type="RNSR">198018249C</idno>
          <idno type="ROR">https://ror.org/04040yw90</idno>
          <orgName>Centre Inria de l'Université de Rennes</orgName>
          <desc>
            <address>
              <addrLine>Campus de beaulieu35042 Rennes cedex</addrLine>
              <country key="FR"/>
            </address>
            <ref type="url">http://www.inria.fr/centre/rennes</ref>
          </desc>
          <listRelation>
            <relation active="#struct-300009" type="direct"/>
          </listRelation>
        </org>
        <org type="institution" xml:id="struct-300009" status="VALID">
          <idno type="ROR">https://ror.org/02kvxyf05</idno>
          <orgName>Institut National de Recherche en Informatique et en Automatique</orgName>
          <orgName type="acronym">Inria</orgName>
          <desc>
            <address>
              <addrLine>Domaine de VoluceauRocquencourt - BP 10578153 Le Chesnay Cedex</addrLine>
              <country key="FR"/>
            </address>
            <ref type="url">http://www.inria.fr/en/</ref>
          </desc>
        </org>
        <org type="regroupinstitution" xml:id="struct-441569" status="VALID">
          <idno type="IdRef">02636817X</idno>
          <idno type="ISNI">0000000122597504</idno>
          <idno type="ROR">https://ror.org/02feahw73</idno>
          <orgName>Centre National de la Recherche Scientifique</orgName>
          <orgName type="acronym">CNRS</orgName>
          <date type="start">1939-10-19</date>
          <desc>
            <address>
              <country key="FR"/>
            </address>
            <ref type="url">https://www.cnrs.fr/</ref>
          </desc>
        </org>
        <org type="institution" xml:id="struct-302845" status="VALID">
          <idno type="IdRef">026380765</idno>
          <idno type="ISNI">0000000107264250</idno>
          <orgName>Direction Générale de l'Aviation Civile</orgName>
          <orgName type="acronym">DGAC</orgName>
          <date type="start">1946-01-01</date>
          <desc>
            <address>
              <country key="FR"/>
            </address>
            <ref type="url">http://www.developpement-durable.gouv.fr/-Secteur-Aerien,1633-.html</ref>
          </desc>
        </org>
      </listOrg>
      <listOrg type="projects">
        <org type="europeanProject" xml:id="projeurop-76104" status="VALID">
          <idno type="number">39584</idno>
          <idno type="program">TREN/07/FP6AE/S07.71574/037180</idno>
          <idno type="call">FP6-AEROSPACE</idno>
          <orgName>IFLY</orgName>
          <desc>Safety, Complexity and Responsibility based design and validation of highly automated Air Traffic Management</desc>
          <date type="start">2007-05-22</date>
          <date type="end">2010-08-21</date>
        </org>
      </listOrg>
    </back>
  </text>
</TEI>