<?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 hal-00141154v1</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="2026-05-03T16:53:28+02:00"/>
      </publicationStmt>
      <sourceDesc>
        <p part="N">HAL API Platform</p>
      </sourceDesc>
    </fileDesc>
  </teiHeader>
  <text>
    <body>
      <listBibl>
        <biblFull>
          <titleStmt>
            <title xml:lang="en">Williams' decomposition of the Lévy continuous random tree and simultaneous extinction probability for populations with neutral mutations</title>
            <author role="aut">
              <persName>
                <forename type="first">Romain</forename>
                <surname>Abraham</surname>
              </persName>
              <email type="md5">76fe4a03b2d1386a3ec4afd13f61a4a1</email>
              <email type="domain">univ-orleans.fr</email>
              <idno type="idhal" notation="string">romain-abraham</idno>
              <idno type="idhal" notation="numeric">7</idno>
              <idno type="halauthorid" notation="string">576-7</idno>
              <idno type="IDREF">https://www.idref.fr/069396787</idno>
              <affiliation ref="#struct-98"/>
            </author>
            <author role="aut">
              <persName>
                <forename type="first">Jean-François</forename>
                <surname>Delmas</surname>
              </persName>
              <email type="md5">5b5ea109c4947344a6313e309a276d50</email>
              <email type="domain">cermics.enpc.fr</email>
              <idno type="idhal" notation="numeric">933972</idno>
              <idno type="halauthorid" notation="string">678503-933972</idno>
              <affiliation ref="#struct-2567"/>
            </author>
            <editor role="depositor">
              <persName>
                <forename>Jean-François</forename>
                <surname>Delmas</surname>
              </persName>
              <email type="md5">5b5ea109c4947344a6313e309a276d50</email>
              <email type="domain">cermics.enpc.fr</email>
            </editor>
          </titleStmt>
          <editionStmt>
            <edition n="v1" type="current">
              <date type="whenSubmitted">2007-04-11 17:50:36</date>
              <date type="whenModified">2025-10-01 14:24:03</date>
              <date type="whenReleased">2007-04-11 21:27:24</date>
              <date type="whenProduced">2007-04-11</date>
              <date type="whenEndEmbargoed">2007-04-11</date>
              <ref type="file" target="https://hal.science/hal-00141154v1/document">
                <date notBefore="2007-04-11"/>
              </ref>
              <ref type="file" subtype="author" n="1" target="https://hal.science/hal-00141154v1/file/williams_04_07.pdf" id="file-141154-351982">
                <date notBefore="2007-04-11"/>
              </ref>
              <ref type="externalLink" target="http://arxiv.org/pdf/0704.1475"/>
            </edition>
            <edition n="v2">
              <date type="whenSubmitted">2009-03-24 11:08:15</date>
            </edition>
            <respStmt>
              <resp>contributor</resp>
              <name key="109524">
                <persName>
                  <forename>Jean-François</forename>
                  <surname>Delmas</surname>
                </persName>
                <email type="md5">5b5ea109c4947344a6313e309a276d50</email>
                <email type="domain">cermics.enpc.fr</email>
              </name>
            </respStmt>
          </editionStmt>
          <publicationStmt>
            <distributor>CCSD</distributor>
            <idno type="halId">hal-00141154</idno>
            <idno type="halUri">https://hal.science/hal-00141154</idno>
            <idno type="halBibtex">abraham:hal-00141154</idno>
            <idno type="halRefHtml">2007</idno>
            <idno type="halRef">2007</idno>
            <availability status="restricted">
              <licence target="https://about.hal.science/hal-authorisation-v1/">HAL Authorization<ref corresp="#file-141154-351982"/></licence>
            </availability>
          </publicationStmt>
          <seriesStmt>
            <idno type="stamp" n="CERMICS" corresp="ENPC">Centre d'Enseignement et de Recherche en Mathématiques, Informatique et Calcul Scientifique</idno>
          </seriesStmt>
          <notesStmt>
            <note type="audience" n="1">Not set</note>
          </notesStmt>
          <sourceDesc>
            <biblStruct>
              <analytic>
                <title xml:lang="en">Williams' decomposition of the Lévy continuous random tree and simultaneous extinction probability for populations with neutral mutations</title>
                <author role="aut">
                  <persName>
                    <forename type="first">Romain</forename>
                    <surname>Abraham</surname>
                  </persName>
                  <email type="md5">76fe4a03b2d1386a3ec4afd13f61a4a1</email>
                  <email type="domain">univ-orleans.fr</email>
                  <idno type="idhal" notation="string">romain-abraham</idno>
                  <idno type="idhal" notation="numeric">7</idno>
                  <idno type="halauthorid" notation="string">576-7</idno>
                  <idno type="IDREF">https://www.idref.fr/069396787</idno>
                  <affiliation ref="#struct-98"/>
                </author>
                <author role="aut">
                  <persName>
                    <forename type="first">Jean-François</forename>
                    <surname>Delmas</surname>
                  </persName>
                  <email type="md5">5b5ea109c4947344a6313e309a276d50</email>
                  <email type="domain">cermics.enpc.fr</email>
                  <idno type="idhal" notation="numeric">933972</idno>
                  <idno type="halauthorid" notation="string">678503-933972</idno>
                  <affiliation ref="#struct-2567"/>
                </author>
              </analytic>
              <monogr>
                <imprint/>
              </monogr>
              <idno type="arxiv">0704.1475</idno>
            </biblStruct>
          </sourceDesc>
          <profileDesc>
            <langUsage>
              <language ident="en">English</language>
            </langUsage>
            <textClass>
              <keywords scheme="author">
                <term xml:lang="en">continuous state branching process</term>
                <term xml:lang="en">immigration</term>
                <term xml:lang="en">continuous random tree</term>
                <term xml:lang="en">Williams' decomposition</term>
                <term xml:lang="en">probability of extinction</term>
                <term xml:lang="en">neutral mutation</term>
              </keywords>
              <classCode scheme="classification">2000 MSC: 60G55, 60J70, 60J80, 92D25</classCode>
              <classCode scheme="halDomain" n="math.math-pr">Mathematics [math]/Probability [math.PR]</classCode>
              <classCode scheme="halTypology" n="UNDEFINED">Preprints, Working Papers, ...</classCode>
              <classCode scheme="halOldTypology" n="UNDEFINED">Preprints, Working Papers, ...</classCode>
              <classCode scheme="halTreeTypology" n="UNDEFINED">Preprints, Working Papers, ...</classCode>
            </textClass>
            <abstract xml:lang="en">
              <p>We consider an initial Eve-population and a population of neutral mutants, such that the total population dies out in finite time. We describe the evolution of the Eve-population and the total population with continuous state branching processes, and the neutral mutation procedure can be seen as an immigration process with intensity proportional to the size of the population. First we establish a Williams' decomposition of the genealogy of the total population given by a continuous random tree, according to the ancestral lineage of the last individual alive. This allows us give a closed formula for the probability of simultaneous extinction of the Eve-population and the total population.</p>
            </abstract>
          </profileDesc>
        </biblFull>
      </listBibl>
    </body>
    <back>
      <listOrg type="structures">
        <org type="laboratory" xml:id="struct-98" status="OLD">
          <idno type="IdRef">161501796</idno>
          <idno type="RNSR">201220243F</idno>
          <orgName>Mathématiques - Analyse, Probabilités, Modélisation - Orléans</orgName>
          <orgName type="acronym">MAPMO</orgName>
          <date type="start">2012-01-01</date>
          <date type="end">2017-12-31</date>
          <desc>
            <address>
              <addrLine>Fédération Denis Poisson, Bâtiment de Mathématiques, B.P. 6759, 45067 Orléans cedex 2</addrLine>
              <country key="FR"/>
            </address>
            <ref type="url">http://www.univ-orleans.fr/mapmo/</ref>
          </desc>
          <listRelation>
            <relation name="UMR 7349" active="#struct-300297" type="direct"/>
            <relation name="UMR7349" active="#struct-441569" type="direct"/>
          </listRelation>
        </org>
        <org type="laboratory" xml:id="struct-2567" status="OLD">
          <orgName>Centre d'Enseignement et de Recherche en Mathématiques, Informatique et Calcul Scientifique</orgName>
          <orgName type="acronym">CERMICS</orgName>
          <desc>
            <address>
              <addrLine>6 et 8 avenue Blaise Pascal Cité Descartes - Champs sur Marne 77455 Marne la Vallée Cedex 2</addrLine>
              <country key="FR"/>
            </address>
            <ref type="url">http://cermics.enpc.fr/</ref>
          </desc>
          <listRelation>
            <relation active="#struct-300009" type="direct"/>
            <relation active="#struct-301545" type="direct"/>
          </listRelation>
        </org>
        <org type="institution" xml:id="struct-300297" status="VALID">
          <idno type="IdRef">026402971</idno>
          <idno type="ISNI">0000 0001 2158 1666</idno>
          <idno type="ROR">https://ror.org/014zrew76</idno>
          <orgName>Université d'Orléans</orgName>
          <orgName type="acronym">UO</orgName>
          <desc>
            <address>
              <addrLine>Château de la Source - Avenue du Parc Floral - BP 6749 - 45067 Orléans cedex 2</addrLine>
              <country key="FR"/>
            </address>
            <ref type="url">http://www.univ-orleans.fr/</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-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="institution" xml:id="struct-301545" status="OLD">
          <idno type="ROR">https://ror.org/02nwvxz07</idno>
          <orgName>École nationale des ponts et chaussées</orgName>
          <orgName type="acronym">ENPC</orgName>
          <date type="start">1747-02-14</date>
          <date type="end">2024-12-31</date>
          <desc>
            <address>
              <addrLine>École nationale des ponts et chaussées, 6-8 avenue Blaise-Pascal, Cité Descartes, Champs-sur-Marne, 77455 Marne-la-Vallée cedex 2</addrLine>
              <country key="FR"/>
            </address>
            <ref type="url">https://ecoledesponts.fr/</ref>
          </desc>
        </org>
      </listOrg>
    </back>
  </text>
</TEI>