Integral representations of solutions for linear stochastic equations with multiplicative perturbances
Identifieur interne : 000415 ( Main/Exploration ); précédent : 000414; suivant : 000416Integral representations of solutions for linear stochastic equations with multiplicative perturbances
Auteurs : M. E. Shaikin [Russie]Source :
- Automation and Remote Control [ 0005-1179 ] ; 2010-04-01.
Abstract
Abstract: We consider the problem of explicitly representing the solutions of multiplicatively perturbed stochastic equations. We represent the solution as an integral Cauchy formula whose transition matrix is random in the case of multiplicative perturbations. Similar to deterministic theory, the transition matrix can be expressed in terms of the fundamental matrix or given by a stochastic Peano series. We give equations for statistical moments of the state vector and explicit integral representations of their solutions. For computing transition matrices of equations on moments, we use some group-theoretical notions and results whose usefulness is illustrated with simple examples.
Url:
DOI: 10.1134/S0005117910040028
Affiliations:
Links toward previous steps (curation, corpus...)
- to stream Istex, to step Corpus: 000742
- to stream Istex, to step Curation: 000742
- to stream Istex, to step Checkpoint: 000371
- to stream Main, to step Merge: 000415
- to stream Main, to step Curation: 000415
Le document en format XML
<record><TEI wicri:istexFullTextTei="biblStruct"><teiHeader><fileDesc><titleStmt><title xml:lang="en">Integral representations of solutions for linear stochastic equations with multiplicative perturbances</title>
<author><name sortKey="Shaikin, M E" sort="Shaikin, M E" uniqKey="Shaikin M" first="M. E." last="Shaikin">M. E. Shaikin</name>
</author>
</titleStmt>
<publicationStmt><idno type="wicri:source">ISTEX</idno>
<idno type="RBID">ISTEX:232577498E910B1D8C234E4A7FFED0E30131A1BB</idno>
<date when="2010" year="2010">2010</date>
<idno type="doi">10.1134/S0005117910040028</idno>
<idno type="url">https://api.istex.fr/document/232577498E910B1D8C234E4A7FFED0E30131A1BB/fulltext/pdf</idno>
<idno type="wicri:Area/Istex/Corpus">000742</idno>
<idno type="wicri:explorRef" wicri:stream="Istex" wicri:step="Corpus" wicri:corpus="ISTEX">000742</idno>
<idno type="wicri:Area/Istex/Curation">000742</idno>
<idno type="wicri:Area/Istex/Checkpoint">000371</idno>
<idno type="wicri:explorRef" wicri:stream="Istex" wicri:step="Checkpoint">000371</idno>
<idno type="wicri:doubleKey">0005-1179:2010:Shaikin M:integral:representations:of</idno>
<idno type="wicri:Area/Main/Merge">000415</idno>
<idno type="wicri:Area/Main/Curation">000415</idno>
<idno type="wicri:Area/Main/Exploration">000415</idno>
</publicationStmt>
<sourceDesc><biblStruct><analytic><title level="a" type="main" xml:lang="en">Integral representations of solutions for linear stochastic equations with multiplicative perturbances</title>
<author><name sortKey="Shaikin, M E" sort="Shaikin, M E" uniqKey="Shaikin M" first="M. E." last="Shaikin">M. E. Shaikin</name>
<affiliation wicri:level="3"><country xml:lang="fr">Russie</country>
<wicri:regionArea>Trapeznikov Institute of Control Sciences, Russian Academy of Sciences, Moscow</wicri:regionArea>
<placeName><settlement type="city">Moscou</settlement>
<region>District fédéral central</region>
</placeName>
</affiliation>
</author>
</analytic>
<monogr></monogr>
<series><title level="j">Automation and Remote Control</title>
<title level="j" type="abbrev">Autom Remote Control</title>
<idno type="ISSN">0005-1179</idno>
<idno type="eISSN">1608-3032</idno>
<imprint><publisher>SP MAIK Nauka/Interperiodica</publisher>
<pubPlace>Dordrecht</pubPlace>
<date type="published" when="2010-04-01">2010-04-01</date>
<biblScope unit="volume">71</biblScope>
<biblScope unit="issue">4</biblScope>
<biblScope unit="page" from="555">555</biblScope>
<biblScope unit="page" to="571">571</biblScope>
</imprint>
<idno type="ISSN">0005-1179</idno>
</series>
</biblStruct>
</sourceDesc>
<seriesStmt><idno type="ISSN">0005-1179</idno>
</seriesStmt>
</fileDesc>
<profileDesc><textClass></textClass>
<langUsage><language ident="en">en</language>
</langUsage>
</profileDesc>
</teiHeader>
<front><div type="abstract" xml:lang="en">Abstract: We consider the problem of explicitly representing the solutions of multiplicatively perturbed stochastic equations. We represent the solution as an integral Cauchy formula whose transition matrix is random in the case of multiplicative perturbations. Similar to deterministic theory, the transition matrix can be expressed in terms of the fundamental matrix or given by a stochastic Peano series. We give equations for statistical moments of the state vector and explicit integral representations of their solutions. For computing transition matrices of equations on moments, we use some group-theoretical notions and results whose usefulness is illustrated with simple examples.</div>
</front>
</TEI>
<affiliations><list><country><li>Russie</li>
</country>
<region><li>District fédéral central</li>
</region>
<settlement><li>Moscou</li>
</settlement>
</list>
<tree><country name="Russie"><region name="District fédéral central"><name sortKey="Shaikin, M E" sort="Shaikin, M E" uniqKey="Shaikin M" first="M. E." last="Shaikin">M. E. Shaikin</name>
</region>
</country>
</tree>
</affiliations>
</record>
Pour manipuler ce document sous Unix (Dilib)
EXPLOR_STEP=$WICRI_ROOT/Wicri/Mathematiques/explor/BourbakiV1/Data/Main/Exploration
HfdSelect -h $EXPLOR_STEP/biblio.hfd -nk 000415 | SxmlIndent | more
Ou
HfdSelect -h $EXPLOR_AREA/Data/Main/Exploration/biblio.hfd -nk 000415 | SxmlIndent | more
Pour mettre un lien sur cette page dans le réseau Wicri
{{Explor lien |wiki= Wicri/Mathematiques |area= BourbakiV1 |flux= Main |étape= Exploration |type= RBID |clé= ISTEX:232577498E910B1D8C234E4A7FFED0E30131A1BB |texte= Integral representations of solutions for linear stochastic equations with multiplicative perturbances }}
This area was generated with Dilib version V0.6.33. |