<?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-00136208</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="2026-05-15T12:28:27+02:00"/>
      </publicationStmt>
      <sourceDesc>
        <p part="N">HAL API Platform</p>
      </sourceDesc>
    </fileDesc>
  </teiHeader>
  <text>
    <body>
      <listBibl>
        <biblFull>
          <titleStmt>
            <title xml:lang="en">Rate of Converrgence for ergodic continuous Markov processes : Lyapunov versus Poincare.</title>
            <author role="aut">
              <persName>
                <forename type="first">Dominique</forename>
                <surname>Bakry</surname>
              </persName>
              <idno type="halauthorid">128086-0</idno>
              <affiliation ref="#struct-92"/>
            </author>
            <author role="aut">
              <persName>
                <forename type="first">Patrick</forename>
                <surname>Cattiaux</surname>
              </persName>
              <email type="md5">c84dce982750cf443a59129cbf57e4df</email>
              <email type="domain">math.univ-toulouse.fr</email>
              <idno type="idhal" notation="string">p-cattiaux</idno>
              <idno type="idhal" notation="numeric">21560</idno>
              <idno type="halauthorid" notation="string">811-21560</idno>
              <idno type="IDREF">https://www.idref.fr/089491319</idno>
              <idno type="ORCID">https://orcid.org/0000-0002-6036-8822</idno>
              <affiliation ref="#struct-101"/>
              <affiliation ref="#struct-89626"/>
            </author>
            <author role="aut">
              <persName>
                <forename type="first">Arnaud</forename>
                <surname>Guillin</surname>
              </persName>
              <email type="md5">3ff4d7728d24789d37cbd292920ea810</email>
              <email type="domain">uca.fr</email>
              <idno type="idhal" notation="string">arnaud-guillin</idno>
              <idno type="idhal" notation="numeric">5334</idno>
              <idno type="halauthorid" notation="string">812-5334</idno>
              <idno type="ORCID">https://orcid.org/0000-0003-2393-6242</idno>
              <idno type="IDREF">https://www.idref.fr/035487976</idno>
              <affiliation ref="#struct-84"/>
            </author>
            <editor role="depositor">
              <persName>
                <forename>Patrick</forename>
                <surname>Cattiaux</surname>
              </persName>
              <email type="md5">c84dce982750cf443a59129cbf57e4df</email>
              <email type="domain">math.univ-toulouse.fr</email>
            </editor>
          </titleStmt>
          <editionStmt>
            <edition n="v1" type="current">
              <date type="whenSubmitted">2007-03-12 19:51:27</date>
              <date type="whenModified">2026-03-23 09:59:13</date>
              <date type="whenReleased">2007-03-12 20:48:01</date>
              <date type="whenProduced">2007-03-12</date>
              <date type="whenEndEmbargoed">2007-03-12</date>
              <ref type="file" target="https://hal.science/hal-00136208v1/document">
                <date notBefore="2007-03-12"/>
              </ref>
              <ref type="file" subtype="author" n="1" target="https://hal.science/hal-00136208v1/file/bcg050307.pdf" id="file-136208-310887">
                <date notBefore="2007-03-12"/>
              </ref>
              <ref type="externalLink" target="http://arxiv.org/pdf/math.PR/0703355"/>
            </edition>
            <respStmt>
              <resp>contributor</resp>
              <name key="103490">
                <persName>
                  <forename>Patrick</forename>
                  <surname>Cattiaux</surname>
                </persName>
                <email type="md5">c84dce982750cf443a59129cbf57e4df</email>
                <email type="domain">math.univ-toulouse.fr</email>
              </name>
            </respStmt>
          </editionStmt>
          <publicationStmt>
            <distributor>CCSD</distributor>
            <idno type="halId">hal-00136208</idno>
            <idno type="halUri">https://hal.science/hal-00136208</idno>
            <idno type="halBibtex">bakry:hal-00136208</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-136208-310887"/></licence>
            </availability>
          </publicationStmt>
          <seriesStmt>
            <idno type="stamp" n="X">École polytechnique</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="LATP" corresp="I2M">Laboratoire d'Analyse, Topologie, Probabilités</idno>
            <idno type="stamp" n="CNRS">CNRS - Centre national de la recherche scientifique</idno>
            <idno type="stamp" n="UNIV-AMU">Aix Marseille Université</idno>
            <idno type="stamp" n="UNIV-PARIS10" corresp="UNIV-PARIS-LUMIERES">Université Paris Nanterre</idno>
            <idno type="stamp" n="INSA-TOULOUSE">Institut National des Sciences Appliquées de Toulouse</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="IMT">Institut de Mathématiques de Toulouse</idno>
            <idno type="stamp" n="CMAP">Centre de Mathématiques Appliquées (CMAP)</idno>
            <idno type="stamp" n="I2M">Institut de Mathématiques de Marseille</idno>
            <idno type="stamp" n="UPN">Collection supérieure de l'université Paris Nanterre</idno>
            <idno type="stamp" n="MODALX" corresp="UNIV-PARIS10">MODAL'X - UMR 9023 - Modélisation aléatoire de Paris Nanterre</idno>
            <idno type="stamp" n="INSA-GROUPE">Groupe INSA</idno>
            <idno type="stamp" n="UNIV-PARIS-LUMIERES"/>
            <idno type="stamp" n="UNIV-PARIS-NANTERRE" corresp="UNIV-PARIS-LUMIERES">Université Paris Nanterre</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="IP-PARIS-DEPARTEMENT-MATHEMATIQUES">Département de Mathèmatiques</idno>
            <idno type="stamp" n="LSP-TLSE"> Laboratoire de Statistique et Probabilités</idno>
          </seriesStmt>
          <notesStmt>
            <note type="audience" n="1">Not set</note>
          </notesStmt>
          <sourceDesc>
            <biblStruct>
              <analytic>
                <title xml:lang="en">Rate of Converrgence for ergodic continuous Markov processes : Lyapunov versus Poincare.</title>
                <author role="aut">
                  <persName>
                    <forename type="first">Dominique</forename>
                    <surname>Bakry</surname>
                  </persName>
                  <idno type="halauthorid">128086-0</idno>
                  <affiliation ref="#struct-92"/>
                </author>
                <author role="aut">
                  <persName>
                    <forename type="first">Patrick</forename>
                    <surname>Cattiaux</surname>
                  </persName>
                  <email type="md5">c84dce982750cf443a59129cbf57e4df</email>
                  <email type="domain">math.univ-toulouse.fr</email>
                  <idno type="idhal" notation="string">p-cattiaux</idno>
                  <idno type="idhal" notation="numeric">21560</idno>
                  <idno type="halauthorid" notation="string">811-21560</idno>
                  <idno type="IDREF">https://www.idref.fr/089491319</idno>
                  <idno type="ORCID">https://orcid.org/0000-0002-6036-8822</idno>
                  <affiliation ref="#struct-101"/>
                  <affiliation ref="#struct-89626"/>
                </author>
                <author role="aut">
                  <persName>
                    <forename type="first">Arnaud</forename>
                    <surname>Guillin</surname>
                  </persName>
                  <email type="md5">3ff4d7728d24789d37cbd292920ea810</email>
                  <email type="domain">uca.fr</email>
                  <idno type="idhal" notation="string">arnaud-guillin</idno>
                  <idno type="idhal" notation="numeric">5334</idno>
                  <idno type="halauthorid" notation="string">812-5334</idno>
                  <idno type="ORCID">https://orcid.org/0000-0003-2393-6242</idno>
                  <idno type="IDREF">https://www.idref.fr/035487976</idno>
                  <affiliation ref="#struct-84"/>
                </author>
              </analytic>
              <monogr>
                <imprint/>
              </monogr>
              <idno type="arxiv">math.PR/0703355</idno>
            </biblStruct>
          </sourceDesc>
          <profileDesc>
            <langUsage>
              <language ident="en">English</language>
            </langUsage>
            <textClass>
              <keywords scheme="author">
                <term xml:lang="en">htpocoercivity</term>
                <term xml:lang="en">Ergodic processes</term>
                <term xml:lang="en">Lyapunov functions</term>
                <term xml:lang="en">Poincare inequalities</term>
                <term xml:lang="en">htpocoercivity.</term>
              </keywords>
              <classCode scheme="classification">26D10, 47D07, 60G10, 60J60.</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 study the relationship between two classical approaches for quantitative ergodic properties : the first one based on Lyapunov type controls and popularized by Meyn and Tweedie, the second one based on functional inequalities (of Poincaré type). We show that they can be linked through new inequalities (Lyapunov-Poincaré inequalities). Explicit examples for diffusion processes are studied, improving some results in the literature. The example of the kinetic Fokker-Planck equation recently studied by Hérau-Nier, Helffer-Nier and Villani is in particular discussed in the final section.</p>
            </abstract>
          </profileDesc>
        </biblFull>
      </listBibl>
    </body>
    <back>
      <listOrg type="structures">
        <org type="laboratory" xml:id="struct-92" status="OLD">
          <idno type="IdRef">026571846</idno>
          <orgName>Laboratoire de Statistique et Probabilités</orgName>
          <orgName type="acronym">LSP</orgName>
          <date type="end">2007-01-01</date>
          <desc>
            <address>
              <addrLine>118 route de Narbonne 31062 Toulouse cedex 09</addrLine>
              <country key="FR"/>
            </address>
            <ref type="url">http://www.lsp.ups-tlse.fr/</ref>
          </desc>
          <listRelation>
            <relation active="#struct-116255" type="direct"/>
            <relation active="#struct-301232" type="indirect"/>
            <relation active="#struct-443875" type="indirect"/>
            <relation active="#struct-217752" type="direct"/>
            <relation name="UMR5583" active="#struct-441569" type="direct"/>
          </listRelation>
        </org>
        <org type="laboratory" xml:id="struct-101" status="VALID">
          <idno type="IdRef">197370497</idno>
          <idno type="RNSR">200114730L</idno>
          <idno type="ROR">https://ror.org/00cjjmc56</idno>
          <orgName>Modélisation aléatoire de Paris X</orgName>
          <orgName type="acronym">MODAL'X</orgName>
          <date type="start">2001-01-01</date>
          <desc>
            <address>
              <addrLine>Université Paris NanterreModal'X, Bâtiment G200 avenue de la république,92000 NANTERRE</addrLine>
              <country key="FR"/>
            </address>
            <ref type="url">http://modalx.parisnanterre.fr/</ref>
          </desc>
          <listRelation>
            <relation name="EA3454" active="#struct-116205" type="direct"/>
            <relation name="UMR9023" active="#struct-441569" type="direct"/>
          </listRelation>
        </org>
        <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="laboratory" xml:id="struct-84" status="OLD">
          <idno type="RNSR">199612403D</idno>
          <orgName>Laboratoire d'Analyse, Topologie, Probabilités</orgName>
          <orgName type="acronym">LATP</orgName>
          <date type="start">2008-01-01</date>
          <date type="end">2011-12-31</date>
          <desc>
            <address>
              <addrLine>39 rue Joliot-Curie 13453 Marseille Cedex 13</addrLine>
              <country key="FR"/>
            </address>
            <ref type="url">http://www.latp.univ-mrs.fr</ref>
          </desc>
          <listRelation>
            <relation active="#struct-27501" type="direct"/>
            <relation active="#struct-92823" type="direct"/>
            <relation name="UMR6632" active="#struct-441569" type="direct"/>
          </listRelation>
        </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="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-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>
        <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-116205" status="VALID">
          <idno type="IdRef">026403587</idno>
          <idno type="ROR">https://ror.org/013bkhk48</idno>
          <orgName>Université Paris Nanterre</orgName>
          <orgName type="acronym">UPN</orgName>
          <date type="start">1970-01-01</date>
          <desc>
            <address>
              <addrLine>200 avenue de la République - 92001 Nanterre cedex</addrLine>
              <country key="FR"/>
            </address>
            <ref type="url">http://www.parisnanterre.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-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="institution" xml:id="struct-27501" status="OLD">
          <idno type="IdRef">026403153</idno>
          <orgName>Université Paul Cézanne - Aix-Marseille 3</orgName>
          <date type="end">2011</date>
          <desc>
            <address>
              <addrLine>3, avenue Robert Schumann - 13628 Aix-en-Provence cedex 1</addrLine>
              <country key="FR"/>
            </address>
            <ref type="url">http://www.univ-cezanne.fr/</ref>
          </desc>
        </org>
        <org type="institution" xml:id="struct-92823" status="OLD">
          <idno type="IdRef">026403781</idno>
          <orgName>Université de Provence - Aix-Marseille 1</orgName>
          <date type="end">2011-12-31</date>
          <desc>
            <address>
              <addrLine>3, place Victor Hugo - 13331 Marseille Cedex 03</addrLine>
              <country key="FR"/>
            </address>
            <ref type="url">http://www.univ-provence.fr/</ref>
          </desc>
        </org>
      </listOrg>
    </back>
  </text>
</TEI>