<?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-01141380v2</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="2026-05-02T20:49:33+02:00"/>
      </publicationStmt>
      <sourceDesc>
        <p part="N">HAL API Platform</p>
      </sourceDesc>
    </fileDesc>
  </teiHeader>
  <text>
    <body>
      <listBibl>
        <biblFull>
          <titleStmt>
            <title xml:lang="en">Regularity structures and renormalisation of FitzHugh-Nagumo SPDEs in three space dimensions</title>
            <author role="aut">
              <persName>
                <forename type="first">Nils</forename>
                <surname>Berglund</surname>
              </persName>
              <email type="md5">47d4500fd0146630dfe5da9c45915238</email>
              <email type="domain">math.cnrs.fr</email>
              <idno type="idhal" notation="string">nils-berglund</idno>
              <idno type="idhal" notation="numeric">290</idno>
              <idno type="halauthorid" notation="string">14399-290</idno>
              <idno type="ARXIV">https://arxiv.org/a/berglund_n_1</idno>
              <idno type="ORCID">https://orcid.org/0000-0001-7044-7885</idno>
              <idno type="IDREF">https://www.idref.fr/109291476</idno>
              <affiliation ref="#struct-24561"/>
              <affiliation ref="#struct-98"/>
            </author>
            <author role="aut">
              <persName>
                <forename type="first">Christian</forename>
                <surname>Kuehn</surname>
              </persName>
              <idno type="halauthorid">508714-0</idno>
              <affiliation ref="#struct-6650"/>
            </author>
            <editor role="depositor">
              <persName>
                <forename>Nils</forename>
                <surname>Berglund</surname>
              </persName>
              <email type="md5">47d4500fd0146630dfe5da9c45915238</email>
              <email type="domain">math.cnrs.fr</email>
            </editor>
          </titleStmt>
          <editionStmt>
            <edition n="v1">
              <date type="whenSubmitted">2015-04-12 12:26:21</date>
            </edition>
            <edition n="v2" type="current">
              <date type="whenSubmitted">2015-06-16 23:18:33</date>
              <date type="whenWritten">2015-06-16</date>
              <date type="whenModified">2026-02-07 05:11:39</date>
              <date type="whenReleased">2015-06-17 09:45:43</date>
              <date type="whenProduced">2016-02-25</date>
              <date type="whenEndEmbargoed">2015-06-16</date>
              <ref type="file" target="https://hal.science/hal-01141380v2/document">
                <date notBefore="2015-06-16"/>
              </ref>
              <ref type="file" subtype="author" n="1" target="https://hal.science/hal-01141380v2/file/fhn_spde_submitted.pdf" id="file-1164459-1249350">
                <date notBefore="2015-06-16"/>
              </ref>
              <ref type="externalLink" target="https://doi.org/10.1214/16-ejp4371"/>
            </edition>
            <respStmt>
              <resp>contributor</resp>
              <name key="101503">
                <persName>
                  <forename>Nils</forename>
                  <surname>Berglund</surname>
                </persName>
                <email type="md5">47d4500fd0146630dfe5da9c45915238</email>
                <email type="domain">math.cnrs.fr</email>
              </name>
            </respStmt>
          </editionStmt>
          <publicationStmt>
            <distributor>CCSD</distributor>
            <idno type="halId">hal-01141380</idno>
            <idno type="halUri">https://hal.science/hal-01141380</idno>
            <idno type="halBibtex">berglund:hal-01141380</idno>
            <idno type="halRefHtml">&lt;i&gt;Electronic Journal of Probability&lt;/i&gt;, 2016, 21 (18), pp.1-48. &lt;a target="_blank" href="https://dx.doi.org/10.1214/16-EJP4371"&gt;&amp;#x27E8;10.1214/16-EJP4371&amp;#x27E9;&lt;/a&gt;</idno>
            <idno type="halRef">Electronic Journal of Probability, 2016, 21 (18), pp.1-48. &amp;#x27E8;10.1214/16-EJP4371&amp;#x27E9;</idno>
            <availability status="restricted">
              <licence target="https://creativecommons.org/licenses/by-sa/4.0/">CC BY-SA 4.0 - Attribution - ShareAlike<ref corresp="#file-1164459-1249350"/></licence>
            </availability>
          </publicationStmt>
          <seriesStmt>
            <idno type="stamp" n="UNIV-TOURS">Université François Rabelais</idno>
            <idno type="stamp" n="CNRS">CNRS - Centre national de la recherche scientifique</idno>
            <idno type="stamp" n="UNIV-ORLEANS">Université d'Orléans</idno>
            <idno type="stamp" n="INSMI">CNRS-INSMI - INstitut des Sciences Mathématiques et de leurs Interactions</idno>
            <idno type="stamp" n="MSL">Modelisation Systemes Langages</idno>
            <idno type="stamp" n="MSL-THESE">Modelisation Systemes Langages</idno>
            <idno type="stamp" n="IDP">Institut Denis Poisson</idno>
            <idno type="stamp" n="TEST3-HALCNRS">TEST3-HALCNRS</idno>
          </seriesStmt>
          <notesStmt>
            <note type="commentary">51 pages</note>
            <note type="audience" n="2">International</note>
            <note type="popular" n="0">No</note>
            <note type="peer" n="1">Yes</note>
          </notesStmt>
          <sourceDesc>
            <biblStruct>
              <analytic>
                <title xml:lang="en">Regularity structures and renormalisation of FitzHugh-Nagumo SPDEs in three space dimensions</title>
                <author role="aut">
                  <persName>
                    <forename type="first">Nils</forename>
                    <surname>Berglund</surname>
                  </persName>
                  <email type="md5">47d4500fd0146630dfe5da9c45915238</email>
                  <email type="domain">math.cnrs.fr</email>
                  <idno type="idhal" notation="string">nils-berglund</idno>
                  <idno type="idhal" notation="numeric">290</idno>
                  <idno type="halauthorid" notation="string">14399-290</idno>
                  <idno type="ARXIV">https://arxiv.org/a/berglund_n_1</idno>
                  <idno type="ORCID">https://orcid.org/0000-0001-7044-7885</idno>
                  <idno type="IDREF">https://www.idref.fr/109291476</idno>
                  <affiliation ref="#struct-24561"/>
                  <affiliation ref="#struct-98"/>
                </author>
                <author role="aut">
                  <persName>
                    <forename type="first">Christian</forename>
                    <surname>Kuehn</surname>
                  </persName>
                  <idno type="halauthorid">508714-0</idno>
                  <affiliation ref="#struct-6650"/>
                </author>
              </analytic>
              <monogr>
                <idno type="halJournalId" status="VALID">765</idno>
                <idno type="issn">1083-6489</idno>
                <title level="j">Electronic Journal of Probability</title>
                <imprint>
                  <publisher>Institute of Mathematical Statistics (IMS)</publisher>
                  <biblScope unit="volume">21</biblScope>
                  <biblScope unit="issue">18</biblScope>
                  <biblScope unit="pp">1-48</biblScope>
                  <date type="datePub">2016-02-25</date>
                </imprint>
              </monogr>
              <idno type="doi">10.1214/16-EJP4371</idno>
              <ref type="publisher">http://projecteuclid.org/euclid.ejp/1456412958</ref>
              <relatedItem target="https://hal.science/hal-01788021v2" type="Requires" subtype="http://purl.org/coar/resource_type/c_6501"/>
            </biblStruct>
          </sourceDesc>
          <profileDesc>
            <langUsage>
              <language ident="en">English</language>
            </langUsage>
            <textClass>
              <keywords scheme="author">
                <term xml:lang="en">regularity structures</term>
                <term xml:lang="en">FitzHugh–Nagumo equation</term>
                <term xml:lang="en">renormalisation</term>
                <term xml:lang="en">reaction–diffusion equations</term>
                <term xml:lang="en">parabolic equations</term>
                <term xml:lang="en">stochastic partial differential equations</term>
              </keywords>
              <classCode scheme="classification">MSC 60H15, 35K57 (primary), 81S20, 82C28 (secondary).</classCode>
              <classCode scheme="halDomain" n="math.math-pr">Mathematics [math]/Probability [math.PR]</classCode>
              <classCode scheme="halTypology" n="ART">Journal articles</classCode>
              <classCode scheme="halOldTypology" n="ART">Journal articles</classCode>
              <classCode scheme="halTreeTypology" n="ART">Journal articles</classCode>
            </textClass>
            <abstract xml:lang="en">
              <p>We prove local existence of solutions for a class of suitably renormalised coupled SPDE–ODE systems driven by space-time white noise, where the space dimension is equal to 2 or 3. This class includes in particular the FitzHugh–Nagumo system describing the evolution of action potentials of a large population of neurons, as well as models with multidimensional gating variables. The proof relies on the theory of regularity structures recently developed by M. Hairer, which is extended to include situations with semigroups that are not regularising in space. We also provide explicit expressions for the renormalisation constants, for a large class of cubic nonlinearities.</p>
            </abstract>
          </profileDesc>
        </biblFull>
      </listBibl>
    </body>
    <back>
      <listOrg type="structures">
        <org type="laboratory" xml:id="struct-24561" status="OLD">
          <idno type="IdRef">161502369</idno>
          <idno type="RNSR">200810694U</idno>
          <orgName>Fédération de recherche Denis Poisson</orgName>
          <orgName type="acronym">FDP</orgName>
          <date type="start">2006-01-01</date>
          <date type="end">2017-12-31</date>
          <desc>
            <address>
              <addrLine>Laboratoire MAPMO rue de Chartres Bât. Maths. - 6759 - 45067 ORLEANS CEDEX 2</addrLine>
              <country key="FR"/>
            </address>
            <ref type="url">http://www.fdpoisson.fr/</ref>
          </desc>
          <listRelation>
            <relation name="FR 2964" active="#struct-300297" type="direct"/>
            <relation name="FR 2964" active="#struct-300298" type="direct"/>
            <relation name="FR2964" active="#struct-441569" type="direct"/>
          </listRelation>
        </org>
        <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-6650" status="VALID">
          <orgName>Institute for Analysis and Scientific Computing [Wien]</orgName>
          <desc>
            <address>
              <addrLine>Wiedner Hauptstr. 8-10, 1040 Wien</addrLine>
              <country key="AT"/>
            </address>
            <ref type="url">http://www.tuwien.ac.at/</ref>
          </desc>
          <listRelation>
            <relation active="#struct-19098" 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="institution" xml:id="struct-300298" status="VALID">
          <idno type="IdRef">026404478</idno>
          <idno type="ISNI">0000000121608742</idno>
          <idno type="ROR">https://ror.org/02wwzvj46</idno>
          <orgName>Université de Tours</orgName>
          <orgName type="acronym">UT</orgName>
          <date type="start">1970-12-17</date>
          <desc>
            <address>
              <addrLine>60 rue du Plat d'Étain, 37020 Tours cedex 1</addrLine>
              <country key="FR"/>
            </address>
            <ref type="url">http://www.univ-tours.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-19098" status="VALID">
          <idno type="IdRef">030036496</idno>
          <idno type="ROR">https://ror.org/04d836q62</idno>
          <orgName>Vienna University of Technology = Technischen Universität Wien</orgName>
          <orgName type="acronym">TU Wien</orgName>
          <desc>
            <address>
              <addrLine>Karlsplatz 13, 1040 Vienna</addrLine>
              <country key="AT"/>
            </address>
            <ref type="url">https://www.tuwien.at/en/</ref>
          </desc>
        </org>
      </listOrg>
    </back>
  </text>
</TEI>