<?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-00948661v3</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="2026-05-26T22:07:30+02:00"/>
      </publicationStmt>
      <sourceDesc>
        <p part="N">HAL API Platform</p>
      </sourceDesc>
    </fileDesc>
  </teiHeader>
  <text>
    <body>
      <listBibl>
        <biblFull>
          <titleStmt>
            <title xml:lang="en">Subgeometric rates of convergence in Wasserstein distance for Markov chains</title>
            <author role="aut">
              <persName>
                <forename type="first">Alain</forename>
                <surname>Durmus</surname>
              </persName>
              <email type="md5">01787fe59d16e0fb55fc0b40a5c095d7</email>
              <email type="domain">gmail.com</email>
              <idno type="idhal" notation="string">alain-oliviero-durmus</idno>
              <idno type="idhal" notation="numeric">1084098</idno>
              <idno type="halauthorid" notation="string">735110-1084098</idno>
              <idno type="ORCID">https://orcid.org/0000-0002-2086-8611</idno>
              <idno type="IDREF">https://www.idref.fr/200536133</idno>
              <affiliation ref="#struct-1006447"/>
            </author>
            <author role="aut">
              <persName>
                <forename type="first">Gersende</forename>
                <surname>Fort</surname>
              </persName>
              <email type="md5">0105f2ffadf3ecbd0e8f52d46f365936</email>
              <email type="domain">math.univ-toulouse.fr</email>
              <idno type="idhal" notation="string">gersende-fort</idno>
              <idno type="idhal" notation="numeric">739303</idno>
              <idno type="halauthorid" notation="string">42736-739303</idno>
              <idno type="ORCID">https://orcid.org/0000-0001-5400-1058</idno>
              <idno type="GOOGLE SCHOLAR">https://scholar.google.com/citations?user=NUoSZ24AAAAJ&amp;hl=fr</idno>
              <idno type="IDREF">https://www.idref.fr/089304969</idno>
              <affiliation ref="#struct-162010"/>
              <affiliation ref="#struct-1954"/>
            </author>
            <author role="aut">
              <persName>
                <forename type="first">Éric</forename>
                <surname>Moulines</surname>
              </persName>
              <email type="md5">6b1231a4aba97c57fa99606c0f031009</email>
              <email type="domain">tsi.enst.fr</email>
              <idno type="idhal" notation="numeric">1350242</idno>
              <idno type="halauthorid" notation="string">1222502-1350242</idno>
              <idno type="ORCID">https://orcid.org/0000-0002-2058-0693</idno>
              <idno type="IDREF">https://www.idref.fr/076452476</idno>
              <idno type="VIAF">https://viaf.org/viaf/190144783095024669712</idno>
              <idno type="ISNI">http://isni.org/isni/000000045491609X</idno>
              <affiliation ref="#struct-162010"/>
            </author>
            <editor role="depositor">
              <persName>
                <forename>Alain</forename>
                <surname>Oliviero-Durmus</surname>
              </persName>
              <email type="md5">01787fe59d16e0fb55fc0b40a5c095d7</email>
              <email type="domain">gmail.com</email>
            </editor>
          </titleStmt>
          <editionStmt>
            <edition n="v1">
              <date type="whenSubmitted">2014-02-18 15:32:31</date>
            </edition>
            <edition n="v2">
              <date type="whenSubmitted">2014-11-06 00:06:02</date>
            </edition>
            <edition n="v3" type="current">
              <date type="whenSubmitted">2015-07-10 19:50:05</date>
              <date type="whenModified">2026-01-19 16:46:18</date>
              <date type="whenReleased">2015-07-15 15:04:47</date>
              <date type="whenProduced">2015-07-10</date>
              <date type="whenEndEmbargoed">2015-07-10</date>
              <ref type="file" target="https://hal.science/hal-00948661v3/document">
                <date notBefore="2015-07-10"/>
              </ref>
              <ref type="file" subtype="author" n="1" target="https://hal.science/hal-00948661v3/file/main.pdf" id="file-1175634-1260202">
                <date notBefore="2015-07-10"/>
              </ref>
            </edition>
            <respStmt>
              <resp>contributor</resp>
              <name key="191627">
                <persName>
                  <forename>Alain</forename>
                  <surname>Oliviero-Durmus</surname>
                </persName>
                <email type="md5">01787fe59d16e0fb55fc0b40a5c095d7</email>
                <email type="domain">gmail.com</email>
              </name>
            </respStmt>
          </editionStmt>
          <publicationStmt>
            <distributor>CCSD</distributor>
            <idno type="halId">hal-00948661</idno>
            <idno type="halUri">https://hal.science/hal-00948661</idno>
            <idno type="halBibtex">durmus:hal-00948661</idno>
            <idno type="halRefHtml">2015</idno>
            <idno type="halRef">2015</idno>
            <availability status="restricted">
              <licence target="https://about.hal.science/hal-authorisation-v1/">HAL Authorization<ref corresp="#file-1175634-1260202"/></licence>
            </availability>
          </publicationStmt>
          <seriesStmt>
            <idno type="stamp" n="SSA">Service de Santé des Armées</idno>
            <idno type="stamp" n="UNIV-TLSE2">Université Toulouse 2</idno>
            <idno type="stamp" n="UNIV-TLSE3">Université de Toulouse</idno>
            <idno type="stamp" n="CNRS">CNRS - Centre national de la recherche scientifique</idno>
            <idno type="stamp" n="ENS-CACHAN">Ecole Normale Supérieure de Cachan</idno>
            <idno type="stamp" n="INSA-TOULOUSE">Institut National des Sciences Appliquées de Toulouse</idno>
            <idno type="stamp" n="ENST">Ecole Nationale Supérieure des Télécommunications</idno>
            <idno type="stamp" n="INSMI">CNRS-INSMI - INstitut des Sciences Mathématiques et de leurs Interactions</idno>
            <idno type="stamp" n="TELECOM-PARISTECH" corresp="PARISTECH">Télécom Paris</idno>
            <idno type="stamp" n="PARISTECH">ParisTech</idno>
            <idno type="stamp" n="IMT">Institut de Mathématiques de Toulouse</idno>
            <idno type="stamp" n="UT1-CAPITOLE">Université Toulouse 1 Capitole</idno>
            <idno type="stamp" n="TELECOM-PARISTECH-SACLAY" corresp="PARISTECH">TELECOM-PARISTECH-SACLAY</idno>
            <idno type="stamp" n="INSA-GROUPE">Groupe INSA</idno>
            <idno type="stamp" n="LTCI" corresp="TELECOM-PARISTECH">Laboratoire Traitement et Communication de l'Information</idno>
            <idno type="stamp" n="INSTITUTS-TELECOM">composantes instituts telecom </idno>
            <idno type="stamp" n="UP-SCIENCES">Université Paris Cité - Faculté des Sciences</idno>
            <idno type="stamp" n="CGB">Centre Giovanni Borelli</idno>
            <idno type="stamp" n="ENS-PARIS-SACLAY">Ecole Normale Supérieure paris-Saclay</idno>
            <idno type="stamp" n="CB_UMR9010">Centre Borelli UMR 9010</idno>
            <idno type="stamp" n="GS-MATHEMATIQUES">Graduate School Mathématiques</idno>
            <idno type="stamp" n="UNIV-UT3">Université Toulouse 3</idno>
            <idno type="stamp" n="UT3-INP">Université de Toulouse / Toulouse INP</idno>
            <idno type="stamp" n="UT3-TOULOUSEINP">Université de Toulouse / Toulouse INP</idno>
            <idno type="stamp" n="INSTITUT-MINES-TELECOM">Institut Mines Telecom</idno>
          </seriesStmt>
          <notesStmt/>
          <sourceDesc>
            <biblStruct>
              <analytic>
                <title xml:lang="en">Subgeometric rates of convergence in Wasserstein distance for Markov chains</title>
                <author role="aut">
                  <persName>
                    <forename type="first">Alain</forename>
                    <surname>Durmus</surname>
                  </persName>
                  <email type="md5">01787fe59d16e0fb55fc0b40a5c095d7</email>
                  <email type="domain">gmail.com</email>
                  <idno type="idhal" notation="string">alain-oliviero-durmus</idno>
                  <idno type="idhal" notation="numeric">1084098</idno>
                  <idno type="halauthorid" notation="string">735110-1084098</idno>
                  <idno type="ORCID">https://orcid.org/0000-0002-2086-8611</idno>
                  <idno type="IDREF">https://www.idref.fr/200536133</idno>
                  <affiliation ref="#struct-1006447"/>
                </author>
                <author role="aut">
                  <persName>
                    <forename type="first">Gersende</forename>
                    <surname>Fort</surname>
                  </persName>
                  <email type="md5">0105f2ffadf3ecbd0e8f52d46f365936</email>
                  <email type="domain">math.univ-toulouse.fr</email>
                  <idno type="idhal" notation="string">gersende-fort</idno>
                  <idno type="idhal" notation="numeric">739303</idno>
                  <idno type="halauthorid" notation="string">42736-739303</idno>
                  <idno type="ORCID">https://orcid.org/0000-0001-5400-1058</idno>
                  <idno type="GOOGLE SCHOLAR">https://scholar.google.com/citations?user=NUoSZ24AAAAJ&amp;hl=fr</idno>
                  <idno type="IDREF">https://www.idref.fr/089304969</idno>
                  <affiliation ref="#struct-162010"/>
                  <affiliation ref="#struct-1954"/>
                </author>
                <author role="aut">
                  <persName>
                    <forename type="first">Éric</forename>
                    <surname>Moulines</surname>
                  </persName>
                  <email type="md5">6b1231a4aba97c57fa99606c0f031009</email>
                  <email type="domain">tsi.enst.fr</email>
                  <idno type="idhal" notation="numeric">1350242</idno>
                  <idno type="halauthorid" notation="string">1222502-1350242</idno>
                  <idno type="ORCID">https://orcid.org/0000-0002-2058-0693</idno>
                  <idno type="IDREF">https://www.idref.fr/076452476</idno>
                  <idno type="VIAF">https://viaf.org/viaf/190144783095024669712</idno>
                  <idno type="ISNI">http://isni.org/isni/000000045491609X</idno>
                  <affiliation ref="#struct-162010"/>
                </author>
              </analytic>
              <monogr>
                <imprint>
                  <date type="datePub">2016-11-01</date>
                </imprint>
              </monogr>
              <idno type="doi">10.1214/15-AIHP699</idno>
            </biblStruct>
          </sourceDesc>
          <profileDesc>
            <langUsage>
              <language ident="en">English</language>
            </langUsage>
            <textClass>
              <keywords scheme="author">
                <term xml:lang="en">rate of convergence</term>
                <term xml:lang="en">Markov chain Monte Carlo in infinite dimension</term>
                <term xml:lang="en">Wasserstein distance</term>
                <term xml:lang="en">Markov chains</term>
              </keywords>
              <classCode scheme="classification">MSC 2010: 60J10, 60B10, 60J05, 60J22, 65C40</classCode>
              <classCode scheme="halDomain" n="math.math-pr">Mathematics [math]/Probability [math.PR]</classCode>
              <classCode scheme="halDomain" n="math.math-st">Mathematics [math]/Statistics [math.ST]</classCode>
              <classCode scheme="halDomain" n="stat.th">Statistics [stat]/Statistics Theory [stat.TH]</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>In this paper, we provide sufficient conditions for the existence of the invariant distribution and for subgeometric rates of convergence in Wasserstein distance for general state-space Markov chains which are (possibly) not irreducible.  Compared to previous work, our approach is based on a purely probabilistic coupling construction which allows to retrieve rates of convergence matching those previously reported for convergence in total variation.    Our results are applied to establish the subgeometric ergodicity in Wasserstein distance of non-linear autoregressive models and of the pre-conditioned Crank-Nicolson Markov chain Monte Carlo algorithm in Hilbert space.</p>
            </abstract>
          </profileDesc>
        </biblFull>
      </listBibl>
    </body>
    <back>
      <listOrg type="structures">
        <org type="laboratory" xml:id="struct-1006447" status="VALID">
          <idno type="IdRef">248391615</idno>
          <idno type="RNSR">202023521J</idno>
          <idno type="ROR">02hcn4061</idno>
          <orgName>CB - Centre Borelli - UMR 9010</orgName>
          <orgName type="acronym">CB</orgName>
          <date type="start">2020-01-01</date>
          <desc>
            <address>
              <addrLine>Campus ENS Paris-Saclay4 Avenue des Sciences,91190 Gif-sur-Yvette</addrLine>
              <country key="FR"/>
            </address>
            <ref type="url">https://centreborelli.ens-paris-saclay.fr/fr</ref>
          </desc>
          <listRelation>
            <relation active="#struct-300092" type="direct"/>
            <relation active="#struct-303623" type="direct"/>
            <relation active="#struct-419361" type="direct"/>
            <relation name="UMR9010" active="#struct-441569" type="direct"/>
            <relation active="#struct-523723" type="direct"/>
            <relation active="#struct-557826" type="direct"/>
          </listRelation>
        </org>
        <org type="laboratory" xml:id="struct-162010" status="OLD">
          <orgName>Laboratoire Traitement et Communication de l'Information</orgName>
          <orgName type="acronym">LTCI</orgName>
          <desc>
            <address>
              <addrLine>46 rue Barrault F-75634 Paris Cedex 13</addrLine>
              <country key="FR"/>
            </address>
            <ref type="url">http://www.ltci.telecom-paristech.fr/</ref>
          </desc>
          <listRelation>
            <relation active="#struct-300362" type="direct"/>
            <relation active="#struct-302102" type="direct"/>
            <relation name="UMR5141" active="#struct-441569" type="direct"/>
          </listRelation>
        </org>
        <org type="laboratory" xml:id="struct-1954" status="OLD">
          <idno type="IdRef">166783900</idno>
          <idno type="ISNI">0000000403836348</idno>
          <idno type="RNSR">200711888W</idno>
          <idno type="ROR">https://ror.org/014vp6c30</idno>
          <orgName>Institut de Mathématiques de Toulouse UMR5219</orgName>
          <orgName type="acronym">IMT</orgName>
          <date type="start">2007-01-01</date>
          <date type="end">2025-01-01</date>
          <desc>
            <address>
              <addrLine>UPS IMT, F-31062 Toulouse Cedex 9, INSA Toulouse, F-31077 Toulouse,France UT1, F-31042 Toulouse, France UT2, F-31058 Toulouse,Téléphone : 05.61.55.67.90</addrLine>
              <country key="FR"/>
            </address>
            <ref type="url">https://www.math.univ-toulouse.fr/</ref>
          </desc>
          <listRelation>
            <relation active="#struct-81148" type="direct"/>
            <relation name="443875" active="#struct-443875" type="indirect"/>
            <relation active="#struct-116255" type="direct"/>
            <relation active="#struct-301232" type="indirect"/>
            <relation active="#struct-443875" type="indirect"/>
            <relation active="#struct-116256" type="direct"/>
            <relation active="#struct-217752" type="direct"/>
            <relation name="UMR5219" active="#struct-441569" type="direct"/>
          </listRelation>
        </org>
        <org type="institution" xml:id="struct-300092" status="VALID">
          <orgName>Service de Santé des Armées</orgName>
          <desc>
            <address>
              <country key="FR"/>
            </address>
            <ref type="url">https://www.defense.gouv.fr/sante</ref>
          </desc>
        </org>
        <org type="institution" xml:id="struct-303623" status="VALID">
          <idno type="IdRef">026388278</idno>
          <idno type="ROR">https://ror.org/02vjkv261</idno>
          <orgName>Institut National de la Santé et de la Recherche Médicale</orgName>
          <orgName type="acronym">INSERM</orgName>
          <desc>
            <address>
              <addrLine>101, rue de Tolbiac, 75013 Paris</addrLine>
              <country key="FR"/>
            </address>
            <ref type="url">http://www.inserm.fr</ref>
          </desc>
        </org>
        <org type="institution" xml:id="struct-419361" status="VALID">
          <idno type="IdRef">241345251</idno>
          <idno type="ROR">https://ror.org/03xjwb503</idno>
          <orgName>Université Paris-Saclay</orgName>
          <desc>
            <address>
              <addrLine>Bâtiment Bréguet, 3 Rue Joliot Curie 2e ét, 91190 Gif-sur-Yvette</addrLine>
              <country key="FR"/>
            </address>
            <ref type="url">https://www.universite-paris-saclay.fr/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-523723" status="VALID">
          <idno type="ROR">https://ror.org/00hx6zz33</idno>
          <orgName>Ecole Normale Supérieure  Paris-Saclay</orgName>
          <orgName type="acronym">ENS Paris Saclay</orgName>
          <desc>
            <address>
              <addrLine>4 avenue des Sciences, 91190 Gif-sur-Yvette</addrLine>
              <country key="FR"/>
            </address>
            <ref type="url">http://ens-paris-saclay.fr/</ref>
          </desc>
        </org>
        <org type="institution" xml:id="struct-557826" status="VALID">
          <idno type="IdRef">236453505</idno>
          <idno type="ISNI">0000 0004 7885 7602</idno>
          <idno type="ROR">https://ror.org/05f82e368</idno>
          <orgName>Université Paris Cité</orgName>
          <orgName type="acronym">UPCité</orgName>
          <date type="start">2020-01-01</date>
          <desc>
            <address>
              <addrLine>85 boulevard Saint-Germain75006 Paris</addrLine>
              <country key="FR"/>
            </address>
            <ref type="url">https://u-paris.fr/</ref>
          </desc>
        </org>
        <org type="institution" xml:id="struct-300362" status="VALID">
          <idno type="ROR">https://ror.org/01naq7912</idno>
          <orgName>Télécom ParisTech</orgName>
          <date type="start">2008-01-01</date>
          <date type="end">2019-06-11</date>
          <desc>
            <address>
              <addrLine>46 rue Barrault 75634 Paris Cedex 13</addrLine>
              <country key="FR"/>
            </address>
            <ref type="url">https://www.telecom-paris.fr</ref>
          </desc>
        </org>
        <org type="regroupinstitution" xml:id="struct-302102" status="VALID">
          <idno type="IdRef">192427156</idno>
          <idno type="ISNI">000000012202567X</idno>
          <idno type="ROR">https://ror.org/025vp2923</idno>
          <idno type="Wikidata">Q27962533</idno>
          <orgName>Institut Mines-Télécom [Paris]</orgName>
          <orgName type="acronym">IMT</orgName>
          <date type="start">2012-03-01</date>
          <desc>
            <address>
              <addrLine>19 Place Marguerite Perey, 91120 Palaiseau</addrLine>
              <country key="FR"/>
            </address>
            <ref type="url">https://www.imt.fr/</ref>
          </desc>
        </org>
        <org type="institution" xml:id="struct-81148" status="VALID">
          <idno type="IdRef">026404354</idno>
          <idno type="ISNI">0000000121902837</idno>
          <idno type="ROR">https://ror.org/0443n9e75</idno>
          <orgName>Université Toulouse Capitole</orgName>
          <orgName type="acronym">UT Capitole</orgName>
          <date type="start">1970-01-01</date>
          <desc>
            <address>
              <addrLine>2 rue du Doyen-Gabriel-Marty - 31042 Toulouse Cedex 9</addrLine>
              <country key="FR"/>
            </address>
            <ref type="url">http://www.ut-capitole.fr/</ref>
          </desc>
          <listRelation>
            <relation name="443875" active="#struct-443875" type="direct"/>
          </listRelation>
        </org>
        <org type="regroupinstitution" xml:id="struct-443875" status="VALID">
          <idno type="ROR">https://ror.org/017tgbk05</idno>
          <orgName>Communauté d'universités et établissements de Toulouse</orgName>
          <orgName type="acronym">Comue de Toulouse</orgName>
          <desc>
            <address>
              <addrLine>41 Allée Jules Guesde, 31000 Toulouse</addrLine>
              <country key="FR"/>
            </address>
            <ref type="url">https://www.univ-toulouse.fr/</ref>
          </desc>
        </org>
        <org type="institution" xml:id="struct-116255" status="VALID">
          <idno type="IdRef">026388766</idno>
          <idno type="ISNI">0000 0001 2286 8343</idno>
          <idno type="ROR">https://ror.org/01h8pf755</idno>
          <idno type="Wikidata">Q858979</idno>
          <orgName>Institut National des Sciences Appliquées - Toulouse</orgName>
          <orgName type="acronym">INSA Toulouse</orgName>
          <date type="start">1963-10-21</date>
          <desc>
            <address>
              <addrLine>135, avenue de Rangueil - 31077 Toulouse cedex 4</addrLine>
              <country key="FR"/>
            </address>
            <ref type="url">http://www.insa-toulouse.fr</ref>
          </desc>
          <listRelation>
            <relation active="#struct-301232" type="direct"/>
            <relation active="#struct-443875" type="direct"/>
          </listRelation>
        </org>
        <org type="regroupinstitution" xml:id="struct-301232" status="VALID">
          <idno type="IdRef">162105150</idno>
          <orgName>Institut National des Sciences Appliquées</orgName>
          <orgName type="acronym">INSA</orgName>
          <desc>
            <address>
              <country key="FR"/>
            </address>
          </desc>
        </org>
        <org type="institution" xml:id="struct-116256" status="VALID">
          <idno type="IdRef">026403994</idno>
          <idno type="ROR">https://ror.org/04ezk3x31</idno>
          <orgName>Université Toulouse - Jean Jaurès</orgName>
          <orgName type="acronym">UT2J</orgName>
          <date type="start">1971-01-01</date>
          <desc>
            <address>
              <addrLine>5 allées Antonio Machado - 31058 Toulouse Cedex 9</addrLine>
              <country key="FR"/>
            </address>
            <ref type="url">http://www.univ-tlse2.fr</ref>
          </desc>
          <listRelation>
            <relation active="#struct-443875" type="direct"/>
          </listRelation>
        </org>
        <org type="institution" xml:id="struct-217752" status="OLD">
          <idno type="IdRef">026404672</idno>
          <idno type="ISNI">0000000121617331</idno>
          <idno type="ROR">https://ror.org/02v6kpv12</idno>
          <idno type="Wikidata">Q1273188</idno>
          <orgName>Université Toulouse III - Paul Sabatier</orgName>
          <orgName type="acronym">UT3</orgName>
          <date type="end">2025-01-01</date>
          <desc>
            <address>
              <addrLine>118 route de Narbonne - 31062 Toulouse</addrLine>
              <country key="FR"/>
            </address>
            <ref type="url">http://www.univ-tlse3.fr/</ref>
          </desc>
          <listRelation>
            <relation active="#struct-443875" type="direct"/>
          </listRelation>
        </org>
      </listOrg>
    </back>
  </text>
</TEI>