<?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-01162547v2</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="2026-05-13T19:35:21+02:00"/>
      </publicationStmt>
      <sourceDesc>
        <p part="N">HAL API Platform</p>
      </sourceDesc>
    </fileDesc>
  </teiHeader>
  <text>
    <body>
      <listBibl>
        <biblFull>
          <titleStmt>
            <title xml:lang="en">Some stochastic models for structured populations : scaling limits and long time  behavior</title>
            <author role="aut">
              <persName>
                <forename type="first">Vincent</forename>
                <surname>Bansaye</surname>
              </persName>
              <email type="md5">c527e35eca0047b2400875cd4a5fbb34</email>
              <email type="domain">ccr.jussieu.fr</email>
              <idno type="idhal" notation="numeric">836664</idno>
              <idno type="halauthorid" notation="string">178883-836664</idno>
              <idno type="IDREF">https://www.idref.fr/134526848</idno>
              <idno type="VIAF">https://viaf.org/viaf/204120785</idno>
              <idno type="ISNI">http://isni.org/isni/0000000358370007</idno>
              <idno type="ORCID">https://orcid.org/0000-0002-7631-3244</idno>
              <affiliation ref="#struct-89626"/>
            </author>
            <author role="aut">
              <persName>
                <forename type="first">Sylvie</forename>
                <surname>Méléard</surname>
              </persName>
              <email type="md5">375e2f805699d50016536341222f43e8</email>
              <email type="domain">polytechnique.edu</email>
              <idno type="idhal" notation="string">sylvie-meleard-sylvie-meleard</idno>
              <idno type="idhal" notation="numeric">843733</idno>
              <idno type="halauthorid" notation="string">114707-843733</idno>
              <idno type="ORCID">https://orcid.org/0000-0001-7125-0398</idno>
              <affiliation ref="#struct-89626"/>
            </author>
            <editor role="depositor">
              <persName>
                <forename>Vincent</forename>
                <surname>Bansaye</surname>
              </persName>
              <email type="md5">eafc02fab2d5cb6ce788d8507322f9cb</email>
              <email type="domain">gmail.com</email>
            </editor>
          </titleStmt>
          <editionStmt>
            <edition n="v1">
              <date type="whenSubmitted">2015-06-10 17:51:39</date>
            </edition>
            <edition n="v2" type="current">
              <date type="whenSubmitted">2017-07-02 21:57:26</date>
              <date type="whenModified">2025-09-04 03:23:29</date>
              <date type="whenReleased">2017-07-05 12:39:51</date>
              <date type="whenProduced">2017-07-02</date>
              <date type="whenEndEmbargoed">2017-07-02</date>
              <ref type="file" target="https://hal.science/hal-01162547v2/document">
                <date notBefore="2017-07-02"/>
              </ref>
              <ref type="file" subtype="author" n="1" target="https://hal.science/hal-01162547v2/file/coursM2-11052017.pdf" id="file-1552439-1609162">
                <date notBefore="2017-07-02"/>
              </ref>
              <ref type="externalLink" target="http://arxiv.org/pdf/1506.04165"/>
            </edition>
            <respStmt>
              <resp>contributor</resp>
              <name key="114452">
                <persName>
                  <forename>Vincent</forename>
                  <surname>Bansaye</surname>
                </persName>
                <email type="md5">eafc02fab2d5cb6ce788d8507322f9cb</email>
                <email type="domain">gmail.com</email>
              </name>
            </respStmt>
          </editionStmt>
          <publicationStmt>
            <distributor>CCSD</distributor>
            <idno type="halId">hal-01162547</idno>
            <idno type="halUri">https://hal.science/hal-01162547</idno>
            <idno type="halBibtex">bansaye:hal-01162547</idno>
            <idno type="halRefHtml">2017</idno>
            <idno type="halRef">2017</idno>
            <availability status="restricted">
              <licence target="https://about.hal.science/hal-authorisation-v1/">HAL Authorization<ref corresp="#file-1552439-1609162"/></licence>
            </availability>
          </publicationStmt>
          <seriesStmt>
            <idno type="stamp" n="X">École polytechnique</idno>
            <idno type="stamp" n="CNRS">CNRS - Centre national de la recherche scientifique</idno>
            <idno type="stamp" n="INSMI">CNRS-INSMI - INstitut des Sciences Mathématiques et de leurs Interactions</idno>
            <idno type="stamp" n="X-CMAP" corresp="X">Centre de Mathématiques Appliquées (CMAP)</idno>
            <idno type="stamp" n="X-DEP-MATHA">Département de mathématiques appliquées de l’École polytechnique</idno>
            <idno type="stamp" n="CMAP">Centre de Mathématiques Appliquées (CMAP)</idno>
            <idno type="stamp" n="UNIV-PARIS-SACLAY">Université Paris-Saclay</idno>
            <idno type="stamp" n="X-SACLAY" corresp="UNIV-PARIS-SACLAY">X-SACLAY</idno>
            <idno type="stamp" n="INRIA2017">INRIA2017</idno>
            <idno type="stamp" n="TEST3-HALCNRS">TEST3-HALCNRS</idno>
            <idno type="stamp" n="DEPARTEMENT-DE-MATHEMATIQUES">Collection du Département de Mathématiques</idno>
          </seriesStmt>
          <notesStmt/>
          <sourceDesc>
            <biblStruct>
              <analytic>
                <title xml:lang="en">Some stochastic models for structured populations : scaling limits and long time  behavior</title>
                <author role="aut">
                  <persName>
                    <forename type="first">Vincent</forename>
                    <surname>Bansaye</surname>
                  </persName>
                  <email type="md5">c527e35eca0047b2400875cd4a5fbb34</email>
                  <email type="domain">ccr.jussieu.fr</email>
                  <idno type="idhal" notation="numeric">836664</idno>
                  <idno type="halauthorid" notation="string">178883-836664</idno>
                  <idno type="IDREF">https://www.idref.fr/134526848</idno>
                  <idno type="VIAF">https://viaf.org/viaf/204120785</idno>
                  <idno type="ISNI">http://isni.org/isni/0000000358370007</idno>
                  <idno type="ORCID">https://orcid.org/0000-0002-7631-3244</idno>
                  <affiliation ref="#struct-89626"/>
                </author>
                <author role="aut">
                  <persName>
                    <forename type="first">Sylvie</forename>
                    <surname>Méléard</surname>
                  </persName>
                  <email type="md5">375e2f805699d50016536341222f43e8</email>
                  <email type="domain">polytechnique.edu</email>
                  <idno type="idhal" notation="string">sylvie-meleard-sylvie-meleard</idno>
                  <idno type="idhal" notation="numeric">843733</idno>
                  <idno type="halauthorid" notation="string">114707-843733</idno>
                  <idno type="ORCID">https://orcid.org/0000-0001-7125-0398</idno>
                  <affiliation ref="#struct-89626"/>
                </author>
              </analytic>
              <monogr>
                <imprint/>
              </monogr>
              <idno type="arxiv">1506.04165</idno>
            </biblStruct>
          </sourceDesc>
          <profileDesc>
            <langUsage>
              <language ident="en">English</language>
            </langUsage>
            <textClass>
              <keywords scheme="author">
                <term xml:lang="en">Scaling limit- Long time behavior -Birth and death processes -large population approx-imations -Continuous state branching processes -Branching processes in random envi-ronment -Measure-valued Markov processes -Martingale properties -Two-level models -Cell division dynamics</term>
              </keywords>
              <classCode scheme="classification">60J80, 60J75, 60G57, 60H10, 92D25, 92D15.</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>The first chapter concerns monotype population models. We first study general birth and death processes and we give non-explosion and extinction criteria, moment computations and a pathwise representation. We then show how different scales may lead to different qualitative approximations, either ODEs or SDEs. The prototypes of these equations are the logistic (deterministic) equation and the logistic Feller diffusion process. The convergence in law of the sequence of processes is proved by tightness-uniqueness argument. In these large population approximations, the competition between individuals leads to nonlinear drift terms. We then focus on models without interaction but including exceptional events due either to demographic stochasticity or to environmental stochasticity. In the first case, an individual may have a large number of offspring and we introduce the class of continuous state branching processes. In the second case, catastrophes may occur and kill a random fraction of the population and the process enjoys a quenched branching property. We emphasize on the study of the Laplace transform, which allows us to classify the long time behavior of these processes. In the second chapter, we model structured populations by measure-valued stochastic differential equations. Our approach is based on the individual dynamics. The individuals are characterized by parameters which have an influence on their survival or reproduction ability. Some of these parameters can be genetic and are inheritable except when mutations occur, but they can also be a space location or a quantity of parasites. The individuals compete for resources or other environmental constraints. We describe the population by a point measure-valued Markov process. We study macroscopic approximations of this process depending on the interplay between different scalings and obtain in the limit either integro-differential equations or reaction-diffusion equations or nonlinear super-processes. In each case, we insist on the specific techniques for the proof of convergence and for the study of the limiting model. The limiting processes offer different models of mutation-selection dynamics. Then, we study two-level models motivated by cell division dynamics, where the cell population is discrete and characterized by a trait, which may be continuous. In 1 particular, we finely study a process for parasite infection and the trait is the parasite load. The latter grows following a Feller diffusion and is randomly shared in the two daughter cells when the cell divides. Finally, we focus on the neutral case when the rate of division of cells is constant but the trait evolves following a general Markov process and may split in a random number of cells. The long time behavior of the structured population is then linked and derived from the behavior a well chosen SDE (monotype population).</p>
            </abstract>
          </profileDesc>
        </biblFull>
      </listBibl>
    </body>
    <back>
      <listOrg type="structures">
        <org type="laboratory" xml:id="struct-89626" status="VALID">
          <idno type="IdRef">197373461</idno>
          <idno type="ISNI">000000010944436X</idno>
          <idno type="RNSR">199719340P</idno>
          <idno type="ROR">https://ror.org/012e1xn46</idno>
          <idno type="Wikidata">Q16008922</idno>
          <orgName>Centre de Mathématiques Appliquées de l'Ecole polytechnique</orgName>
          <orgName type="acronym">CMAP</orgName>
          <date type="start">2005-01-01</date>
          <desc>
            <address>
              <addrLine>Route de Saclay, 91128 Palaiseau Cedex</addrLine>
              <country key="FR"/>
            </address>
            <ref type="url">https://cmap.ip-paris.fr/</ref>
          </desc>
          <listRelation>
            <relation active="#struct-300009" type="direct"/>
            <relation active="#struct-300340" type="direct"/>
            <relation active="#struct-563936" type="indirect"/>
            <relation name="UMR7641" active="#struct-441569" 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="institution" xml:id="struct-300340" status="VALID">
          <idno type="IdRef">027309320</idno>
          <idno type="ISNI">0000000121581279</idno>
          <idno type="ROR">https://ror.org/05hy3tk52</idno>
          <idno type="Wikidata">Q273626</idno>
          <orgName>École polytechnique</orgName>
          <orgName type="acronym">X</orgName>
          <date type="start">1794-03-11</date>
          <desc>
            <address>
              <addrLine>Route de Saclay, 91128 Palaiseau Cedex</addrLine>
              <country key="FR"/>
            </address>
            <ref type="url">https://www.polytechnique.edu/</ref>
          </desc>
          <listRelation>
            <relation active="#struct-563936" type="direct"/>
          </listRelation>
        </org>
        <org type="regroupinstitution" xml:id="struct-563936" status="VALID">
          <idno type="IdRef">238327159</idno>
          <idno type="ISNI">0000000502717600</idno>
          <idno type="ROR">https://ror.org/042tfbd02</idno>
          <idno type="Wikidata">Q48759778</idno>
          <orgName>Institut Polytechnique de Paris</orgName>
          <orgName type="acronym">IP Paris</orgName>
          <date type="start">2019-06-02</date>
          <desc>
            <address>
              <addrLine>Route de Saclay, 91120 Palaiseau Cedex, France</addrLine>
              <country key="FR"/>
            </address>
            <ref type="url">https://www.ip-paris.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>
      </listOrg>
    </back>
  </text>
</TEI>