<?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-00091310</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="2026-05-16T03:03:30+02:00"/>
      </publicationStmt>
      <sourceDesc>
        <p part="N">HAL API Platform</p>
      </sourceDesc>
    </fileDesc>
  </teiHeader>
  <text>
    <body>
      <listBibl>
        <biblFull>
          <titleStmt>
            <title xml:lang="en">m-order integrals and generalized Ito's formula; the case of a fractional Brownian motion with any Hurst index</title>
            <author role="aut">
              <persName>
                <forename type="first">Mihai</forename>
                <surname>Gradinaru</surname>
              </persName>
              <email type="md5">fd58494b0cdfe78a4eeaf5f7df371c16</email>
              <email type="domain">iecn.u-nancy.fr</email>
              <idno type="idhal" notation="numeric">832590</idno>
              <idno type="halauthorid" notation="string">132696-832590</idno>
              <affiliation ref="#struct-23"/>
            </author>
            <author role="aut">
              <persName>
                <forename type="first">Ivan</forename>
                <surname>Nourdin</surname>
              </persName>
              <email type="md5">27bf831796793fe9a55d359aace1aab2</email>
              <email type="domain">ccr.jusssieu.fr</email>
              <idno type="idhal" notation="numeric">834810</idno>
              <idno type="halauthorid" notation="string">116071-834810</idno>
              <affiliation ref="#struct-23"/>
              <affiliation ref="#struct-102"/>
            </author>
            <author role="aut">
              <persName>
                <forename type="first">Francesco</forename>
                <surname>Russo</surname>
              </persName>
              <email type="md5">e4fe980d922333f50cbd29e932987934</email>
              <email type="domain">math.univ-paris13.fr</email>
              <idno type="idhal" notation="string">francesco-russo</idno>
              <idno type="idhal" notation="numeric">4507</idno>
              <idno type="halauthorid" notation="string">11541-4507</idno>
              <idno type="IDREF">https://www.idref.fr/066847133</idno>
              <idno type="ORCID">https://orcid.org/0000-0002-9890-7465</idno>
              <orgName ref="#struct-300065"/>
              <affiliation ref="#struct-78"/>
            </author>
            <author role="aut">
              <persName>
                <forename type="first">Pierre</forename>
                <surname>Vallois</surname>
              </persName>
              <email type="md5">8bc3143eb6d343c25802238e5d767a2b</email>
              <email type="domain">iecn.u-nancy.fr</email>
              <idno type="idhal" notation="string">pierre-vallois</idno>
              <idno type="idhal" notation="numeric">931130</idno>
              <idno type="halauthorid" notation="string">133071-931130</idno>
              <affiliation ref="#struct-23"/>
              <affiliation ref="#struct-2489"/>
            </author>
            <editor role="depositor">
              <persName>
                <forename>Mihai</forename>
                <surname>Gradinaru</surname>
              </persName>
              <email type="md5">6d2e3d0261678bd583f59d4ebc713aec</email>
              <email type="domain">univ-rennes1.fr</email>
            </editor>
          </titleStmt>
          <editionStmt>
            <edition n="v1" type="current">
              <date type="whenSubmitted">2006-09-05 17:20:05</date>
              <date type="whenWritten">2005</date>
              <date type="whenModified">2026-04-01 03:13:18</date>
              <date type="whenReleased">2006-09-05 18:32:24</date>
              <date type="whenProduced">2005</date>
              <date type="whenEndEmbargoed">2006-09-05</date>
              <ref type="file" target="https://hal.science/hal-00091310v1/document">
                <date notBefore="2006-09-05"/>
              </ref>
              <ref type="file" n="1" target="https://hal.science/hal-00091310v1/file/m-inte-ito.pdf" id="file-91310-743708">
                <date notBefore="2006-09-05"/>
              </ref>
              <ref type="externalLink" target="http://www.numdam.org/article/AIHPB_2005__41_4_781_0.pdf"/>
            </edition>
            <respStmt>
              <resp>contributor</resp>
              <name key="109514">
                <persName>
                  <forename>Mihai</forename>
                  <surname>Gradinaru</surname>
                </persName>
                <email type="md5">6d2e3d0261678bd583f59d4ebc713aec</email>
                <email type="domain">univ-rennes1.fr</email>
              </name>
            </respStmt>
          </editionStmt>
          <publicationStmt>
            <distributor>CCSD</distributor>
            <idno type="halId">hal-00091310</idno>
            <idno type="halUri">https://hal.science/hal-00091310</idno>
            <idno type="halBibtex">gradinaru:hal-00091310</idno>
            <idno type="halRefHtml">&lt;i&gt;Annales de l'Institut Henri Poincaré (B) Probabilités et Statistiques&lt;/i&gt;, 2005, 41, pp.781-806. &lt;a target="_blank" href="https://dx.doi.org/10.1016/j.anihpb.2004.06.002"&gt;&amp;#x27E8;10.1016/j.anihpb.2004.06.002&amp;#x27E9;&lt;/a&gt;</idno>
            <idno type="halRef">Annales de l'Institut Henri Poincaré (B) Probabilités et Statistiques, 2005, 41, pp.781-806. &amp;#x27E8;10.1016/j.anihpb.2004.06.002&amp;#x27E9;</idno>
            <availability status="restricted">
              <licence target="https://about.hal.science/hal-authorisation-v1/">HAL Authorization<ref corresp="#file-91310-743708"/></licence>
            </availability>
          </publicationStmt>
          <seriesStmt>
            <idno type="stamp" n="UNIV-PARIS7" corresp="UNIV-PARIS">Université Denis Diderot - Paris VII</idno>
            <idno type="stamp" n="UNIV-PARIS13">Université Paris-Nord - Paris XIII </idno>
            <idno type="stamp" n="UPMC" corresp="SORBONNE-UNIVERSITE">Université Pierre et Marie Curie</idno>
            <idno type="stamp" n="UNIV-PARIS8" corresp="UNIV-PARIS-LUMIERES">Université Paris VIII Vincennes-Saint Denis</idno>
            <idno type="stamp" n="PMA" corresp="SORBONNE-UNIVERSITE">Laboratoire de Probabilités et Modèles Aléatoires</idno>
            <idno type="stamp" n="CNRS">CNRS - Centre national de la recherche scientifique</idno>
            <idno type="stamp" n="INRIA">INRIA - Institut National de Recherche en Informatique et en Automatique</idno>
            <idno type="stamp" n="INPL">Institut National Polytechnique de Lorraine</idno>
            <idno type="stamp" n="INRIA-SOPHIA">INRIA Sophia Antipolis - Méditerranée</idno>
            <idno type="stamp" n="LAGA" corresp="UNIV-PARIS13">Laboratoire d'Analyse, Géométrie et Applications</idno>
            <idno type="stamp" n="IECN">IECL - Institut Elie Cartan de Lorraine</idno>
            <idno type="stamp" n="OCA">Observatoire de la Cote d'Azur</idno>
            <idno type="stamp" n="INRIASO">INRIA-SOPHIA</idno>
            <idno type="stamp" n="INRIA_TEST">INRIA - Institut National de Recherche en Informatique et en Automatique</idno>
            <idno type="stamp" n="TESTALAIN1">TESTALAIN1</idno>
            <idno type="stamp" n="UNIV-LORRAINE">Université de Lorraine</idno>
            <idno type="stamp" n="INRIA2">INRIA 2</idno>
            <idno type="stamp" n="UPMC_POLE_1" corresp="UPMC">UPMC Pôle 1</idno>
            <idno type="stamp" n="GALILE" corresp="UNIV-PARIS13">Institut Galilée Université Paris 13</idno>
            <idno type="stamp" n="UNIV-COTEDAZUR">Université Côte d'Azur</idno>
            <idno type="stamp" n="LPSM" corresp="SORBONNE-UNIVERSITE">Laboratoire de Probabilités, Statistique et Modélisation</idno>
            <idno type="stamp" n="SORBONNE-UNIVERSITE">Sorbonne Université</idno>
            <idno type="stamp" n="SU-SCIENCES" corresp="SORBONNE-UNIVERSITE">Faculté des Sciences de Sorbonne Université</idno>
            <idno type="stamp" n="UNIV-PARIS-LUMIERES"/>
            <idno type="stamp" n="IBHGC" corresp="UNIV-PARIS13">Institut de Biomécanique Humaine Georges Charpak</idno>
            <idno type="stamp" n="SORBONNE-PARIS-NORD">Université Sorbonne Paris Nord</idno>
            <idno type="stamp" n="UNIV-PARIS">Université Paris Cité</idno>
            <idno type="stamp" n="SU-TI">Sorbonne Université - Texte Intégral</idno>
            <idno type="stamp" n="UNIV-PARIS8-OA" corresp="UNIV-PARIS8">HAL UNIV-PARIS8 - open access</idno>
            <idno type="stamp" n="ALLIANCE-SU"> Alliance Sorbonne Université</idno>
            <idno type="stamp" n="ACT-R" corresp="UNIV-PARIS13">Act'R </idno>
            <idno type="stamp" n="AM2I-UL">Pôle scientifique Automatique, Mathématiques, Informatique et leurs Intéractions de l'Université de Lorraine</idno>
          </seriesStmt>
          <notesStmt>
            <note type="audience" n="1">Not set</note>
            <note type="popular" n="0">No</note>
            <note type="peer" n="1">Yes</note>
          </notesStmt>
          <sourceDesc>
            <biblStruct>
              <analytic>
                <title xml:lang="en">m-order integrals and generalized Ito's formula; the case of a fractional Brownian motion with any Hurst index</title>
                <author role="aut">
                  <persName>
                    <forename type="first">Mihai</forename>
                    <surname>Gradinaru</surname>
                  </persName>
                  <email type="md5">fd58494b0cdfe78a4eeaf5f7df371c16</email>
                  <email type="domain">iecn.u-nancy.fr</email>
                  <idno type="idhal" notation="numeric">832590</idno>
                  <idno type="halauthorid" notation="string">132696-832590</idno>
                  <affiliation ref="#struct-23"/>
                </author>
                <author role="aut">
                  <persName>
                    <forename type="first">Ivan</forename>
                    <surname>Nourdin</surname>
                  </persName>
                  <email type="md5">27bf831796793fe9a55d359aace1aab2</email>
                  <email type="domain">ccr.jusssieu.fr</email>
                  <idno type="idhal" notation="numeric">834810</idno>
                  <idno type="halauthorid" notation="string">116071-834810</idno>
                  <affiliation ref="#struct-23"/>
                  <affiliation ref="#struct-102"/>
                </author>
                <author role="aut">
                  <persName>
                    <forename type="first">Francesco</forename>
                    <surname>Russo</surname>
                  </persName>
                  <email type="md5">e4fe980d922333f50cbd29e932987934</email>
                  <email type="domain">math.univ-paris13.fr</email>
                  <idno type="idhal" notation="string">francesco-russo</idno>
                  <idno type="idhal" notation="numeric">4507</idno>
                  <idno type="halauthorid" notation="string">11541-4507</idno>
                  <idno type="IDREF">https://www.idref.fr/066847133</idno>
                  <idno type="ORCID">https://orcid.org/0000-0002-9890-7465</idno>
                  <orgName ref="#struct-300065"/>
                  <affiliation ref="#struct-78"/>
                </author>
                <author role="aut">
                  <persName>
                    <forename type="first">Pierre</forename>
                    <surname>Vallois</surname>
                  </persName>
                  <email type="md5">8bc3143eb6d343c25802238e5d767a2b</email>
                  <email type="domain">iecn.u-nancy.fr</email>
                  <idno type="idhal" notation="string">pierre-vallois</idno>
                  <idno type="idhal" notation="numeric">931130</idno>
                  <idno type="halauthorid" notation="string">133071-931130</idno>
                  <affiliation ref="#struct-23"/>
                  <affiliation ref="#struct-2489"/>
                </author>
              </analytic>
              <monogr>
                <idno type="halJournalId" status="OLD">38274</idno>
                <idno type="issn">0020-2347</idno>
                <title level="j">Annales de l'Institut Henri Poincaré (B) Probabilités et Statistiques</title>
                <imprint>
                  <publisher>Institut Henri Poincaré (IHP)</publisher>
                  <biblScope unit="volume">41</biblScope>
                  <biblScope unit="pp">781-806</biblScope>
                  <date type="datePub">2005</date>
                </imprint>
              </monogr>
              <idno type="doi">10.1016/j.anihpb.2004.06.002</idno>
            </biblStruct>
          </sourceDesc>
          <profileDesc>
            <langUsage>
              <language ident="en">English</language>
            </langUsage>
            <textClass>
              <keywords scheme="author">
                <term xml:lang="en">m-order integral</term>
                <term xml:lang="en">Itô's formula</term>
                <term xml:lang="en">Fractional Brownian motion</term>
              </keywords>
              <classCode scheme="classification">60H05; 60G15; 60G18</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>Given an integer m, a probability measure ν on [0,1], a process X and a real function g, we define the m-order ν-integral having as integrator X and as integrand g(X). In the case of the fractional Brownian motion B, for any locally bounded function g, the corresponding integral vanishes for all odd indices m&gt;1/2H and any symmetric ν. One consequence is an Itô–Stratonovich type expansion for the fractional Brownian motion with arbitrary Hurst index 01/6.</p>
            </abstract>
          </profileDesc>
        </biblFull>
      </listBibl>
    </body>
    <back>
      <listOrg type="structures">
        <org type="laboratory" xml:id="struct-23" status="OLD">
          <orgName>Institut Élie Cartan de Nancy</orgName>
          <orgName type="acronym">IECN</orgName>
          <date type="end">2012-12-31</date>
          <desc>
            <address>
              <addrLine>Université Henri Poincaré, Campus Scientifique, boulevard des Aiguillettes, 54000 Vandoeuvre-les-Nancy</addrLine>
              <country key="FR"/>
            </address>
            <ref type="url">http://www.iecn.u-nancy.fr/</ref>
          </desc>
          <listRelation>
            <relation active="#struct-300009" type="direct"/>
            <relation active="#struct-300291" type="direct"/>
            <relation active="#struct-300292" type="direct"/>
            <relation active="#struct-300293" type="direct"/>
            <relation name="UMR7502 / UMR9973" active="#struct-441569" type="direct"/>
          </listRelation>
        </org>
        <org type="laboratory" xml:id="struct-102" status="OLD">
          <idno type="RNSR">199712645M</idno>
          <orgName>Laboratoire de Probabilités et Modèles Aléatoires</orgName>
          <orgName type="acronym">LPMA</orgName>
          <date type="end">2017-12-31</date>
          <desc>
            <address>
              <country key="FR"/>
            </address>
            <ref type="url">http://www.proba.jussieu.fr/</ref>
          </desc>
          <listRelation>
            <relation active="#struct-93591" type="direct"/>
            <relation active="#struct-300301" type="direct"/>
            <relation name="UMR7599" active="#struct-441569" type="direct"/>
          </listRelation>
        </org>
        <org type="laboratory" xml:id="struct-78" status="OLD">
          <idno type="IdRef">086041142</idno>
          <idno type="ISNI">0000000106421613</idno>
          <idno type="RNSR">199712596J</idno>
          <idno type="ROR">https://ror.org/018nzqy79</idno>
          <orgName>Laboratoire Analyse, Géométrie et Applications</orgName>
          <orgName type="acronym">LAGA</orgName>
          <date type="start">1997-01-01</date>
          <date type="end">2019-12-31</date>
          <desc>
            <address>
              <addrLine>Institut Galilée, Université Paris 13, 99 avenue Jean-Baptiste Clément, F-93430, Villetaneuse, France</addrLine>
              <country key="FR"/>
            </address>
            <ref type="url">http://www.math.univ-paris13.fr/laga/</ref>
          </desc>
          <listRelation>
            <relation name="UMR7539" active="#struct-11141" type="direct"/>
            <relation name="UMR7539" active="#struct-15786" type="direct"/>
            <relation active="#struct-301340" type="direct"/>
            <relation name="UMR7539" active="#struct-441569" type="direct"/>
          </listRelation>
        </org>
        <org type="researchteam" xml:id="struct-2489" status="OLD">
          <idno type="RNSR">199421411D</idno>
          <orgName>Probabilistic numerical methods</orgName>
          <orgName type="acronym">OMEGA</orgName>
          <desc>
            <address>
              <country key="FR"/>
            </address>
          </desc>
          <listRelation>
            <relation active="#struct-34586" type="direct"/>
            <relation active="#struct-300009" type="indirect"/>
            <relation active="#struct-300291" type="direct"/>
            <relation active="#struct-300292" type="direct"/>
            <relation name="UMR7502" 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-300291" status="OLD">
          <orgName>Université Henri Poincaré - Nancy 1</orgName>
          <orgName type="acronym">UHP</orgName>
          <date type="end">2011-12-31</date>
          <desc>
            <address>
              <addrLine>24-30 rue Lionnois, BP 60120, 54 003 NANCY cedex, France</addrLine>
              <country key="FR"/>
            </address>
          </desc>
        </org>
        <org type="institution" xml:id="struct-300292" status="OLD">
          <orgName>Université Nancy 2</orgName>
          <date type="end">2011-12-31</date>
          <desc>
            <address>
              <addrLine>91 avenue de la Libération, BP 454, 54001 Nancy cedex</addrLine>
              <country key="FR"/>
            </address>
          </desc>
        </org>
        <org type="institution" xml:id="struct-300293" status="OLD">
          <orgName>Institut National Polytechnique de Lorraine</orgName>
          <orgName type="acronym">INPL</orgName>
          <date type="end">2011-12-31</date>
          <desc>
            <address>
              <country key="FR"/>
            </address>
          </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-93591" status="OLD">
          <idno type="ROR">https://ror.org/02en5vm52</idno>
          <orgName>Université Pierre et Marie Curie - Paris 6</orgName>
          <orgName type="acronym">UPMC</orgName>
          <date type="end">2017-12-31</date>
          <desc>
            <address>
              <addrLine>4 place Jussieu - 75005 Paris</addrLine>
              <country key="FR"/>
            </address>
            <ref type="url">http://www.upmc.fr/</ref>
          </desc>
        </org>
        <org type="institution" xml:id="struct-300301" status="OLD">
          <idno type="IdRef">027542084</idno>
          <idno type="ISNI">0000000121514068</idno>
          <idno type="ROR">https://ror.org/02n7qrg46</idno>
          <orgName>Université Paris Diderot - Paris 7</orgName>
          <orgName type="acronym">UPD7</orgName>
          <date type="end">2019-12-31</date>
          <desc>
            <address>
              <addrLine>5 rue Thomas-Mann - 75205 Paris cedex 13</addrLine>
              <country key="FR"/>
            </address>
            <ref type="url">http://www.univ-paris-diderot.fr</ref>
          </desc>
        </org>
        <org type="institution" xml:id="struct-11141" status="VALID">
          <idno type="IdRef">026403552</idno>
          <idno type="ISNI">0000000121083026</idno>
          <idno type="ROR">https://ror.org/04wez5e68</idno>
          <orgName>Université Paris 8</orgName>
          <orgName type="acronym">UP8</orgName>
          <date type="start">1971-01-01</date>
          <desc>
            <address>
              <addrLine>2 rue de la Liberté - 93526 Saint-Denis cedex</addrLine>
              <country key="FR"/>
            </address>
            <ref type="url">http://www.univ-paris8.fr/</ref>
          </desc>
        </org>
        <org type="institution" xml:id="struct-15786" status="VALID">
          <idno type="ROR">https://ror.org/05f82e368</idno>
          <orgName>Université Paris 13</orgName>
          <orgName type="acronym">UP13</orgName>
          <desc>
            <address>
              <country key="FR"/>
            </address>
            <ref type="url">http://www.univ-paris13.fr/</ref>
          </desc>
        </org>
        <org type="institution" xml:id="struct-301340" status="VALID">
          <orgName>Institut Galilée</orgName>
          <desc>
            <address>
              <country key="FR"/>
            </address>
          </desc>
        </org>
        <org type="laboratory" xml:id="struct-34586" status="VALID">
          <idno type="RNSR">198318250R</idno>
          <idno type="ROR">https://ror.org/01nzkaw91</idno>
          <orgName>Centre Inria d'Université Côte d'Azur</orgName>
          <desc>
            <address>
              <addrLine>2004 route des Lucioles BP 93 06902 Sophia Antipolis</addrLine>
              <country key="FR"/>
            </address>
            <ref type="url">http://www.inria.fr/centre/sophia/</ref>
          </desc>
          <listRelation>
            <relation active="#struct-300009" type="direct"/>
          </listRelation>
        </org>
      </listOrg>
    </back>
  </text>
</TEI>