Long-time behavior of stochastic evolution equations with multiplicative rough noise

Kurzanzeige
dc.contributor.authorSeitz, Tim
dc.date.accessioned2025-11-13T06:32:55Z
dc.date.available2025-11-13T06:32:55Z
dc.date.issued2025
dc.description.abstractThis thesis primarily investigates stochastic evolution equations with nonlinear multiplicative noise and their long-term behavior. Due to the stochastic influence, the solutions are, in general, not pathwise defined, which causes several problems when examining long-term behavior. In particular, it is challenging to consider equations with nonlinear multiplicative noise. For this reason, the focus of this work is on pathwise solution concepts. To be more precise, we consider mild solutions using the theory of rough paths and pathwise mild solutions. The results are applied to several examples, such as equations with noise on the boundary. We also highlight some open questions or potential areas for extension.
dc.description.versionpublisheddeu
dc.identifier.ppn1941071988
dc.identifier.urihttps://kops.uni-konstanz.de/handle/123456789/75200
dc.language.isoeng
dc.rightsCC0 1.0 Universalen
dc.rights.urihttp://creativecommons.org/publicdomain/zero/1.0/
dc.subjectrough partial differential equations
dc.subjectmild Gronwall lemma
dc.subjectLyapunov exponents
dc.subjectrough boundary noise
dc.subjectsingular Gronwall inequality
dc.subjectrandom pullback
dc.subjectstochastic partial differential equations
dc.subjectcontrolled rough paths
dc.subjectextrapolation operators
dc.subjectNeumann boundary noise.
dc.subjectpathwise mild solutions
dc.subjectrandom dynamical systems
dc.subjectnon-autonomuous rough partial differential equations
dc.subject.ddc510
dc.titleLong-time behavior of stochastic evolution equations with multiplicative rough noiseeng
dc.typeDOCTORAL_THESIS
dspace.entity.typePublication
kops.citation.bibtex
@phdthesis{Seitz2025Longt-75200,
  title={Long-time behavior of stochastic evolution equations with multiplicative rough noise},
  year={2025},
  author={Seitz, Tim},
  address={Konstanz},
  school={Universität Konstanz}
}
kops.citation.iso690SEITZ, Tim, 2025. Long-time behavior of stochastic evolution equations with multiplicative rough noise [Dissertation]. Konstanz: Universität Konstanzdeu
kops.citation.iso690SEITZ, Tim, 2025. Long-time behavior of stochastic evolution equations with multiplicative rough noise [Dissertation]. Konstanz: University of Konstanzeng
kops.citation.rdf
<rdf:RDF
    xmlns:dcterms="http://purl.org/dc/terms/"
    xmlns:dc="http://purl.org/dc/elements/1.1/"
    xmlns:rdf="http://www.w3.org/1999/02/22-rdf-syntax-ns#"
    xmlns:bibo="http://purl.org/ontology/bibo/"
    xmlns:dspace="http://digital-repositories.org/ontologies/dspace/0.1.0#"
    xmlns:foaf="http://xmlns.com/foaf/0.1/"
    xmlns:void="http://rdfs.org/ns/void#"
    xmlns:xsd="http://www.w3.org/2001/XMLSchema#" > 
  <rdf:Description rdf:about="https://kops.uni-konstanz.de/server/rdf/resource/123456789/75200">
    <void:sparqlEndpoint rdf:resource="http://localhost/fuseki/dspace/sparql"/>
    <dspace:isPartOfCollection rdf:resource="https://kops.uni-konstanz.de/server/rdf/resource/123456789/39"/>
    <bibo:uri rdf:resource="https://kops.uni-konstanz.de/handle/123456789/75200"/>
    <dcterms:rights rdf:resource="http://creativecommons.org/publicdomain/zero/1.0/"/>
    <dcterms:isPartOf rdf:resource="https://kops.uni-konstanz.de/server/rdf/resource/123456789/39"/>
    <dc:creator>Seitz, Tim</dc:creator>
    <dc:language>eng</dc:language>
    <dcterms:abstract>This thesis primarily investigates stochastic evolution equations with nonlinear multiplicative noise and their long-term behavior. Due to the stochastic influence, the solutions are, in general, not pathwise defined, which causes several problems when examining long-term behavior. In particular, it is challenging to consider equations with nonlinear multiplicative noise. For this reason, the focus of this work is on pathwise solution concepts. To be more precise, we consider mild solutions using the theory of rough paths and pathwise mild solutions. The results are applied to several examples, such as equations with noise on the boundary. We also highlight some open questions or potential areas for extension.</dcterms:abstract>
    <dcterms:hasPart rdf:resource="https://kops.uni-konstanz.de/bitstream/123456789/75200/4/Seitz_2-1ufr4kqxtyqhm4.pdf"/>
    <dcterms:available rdf:datatype="http://www.w3.org/2001/XMLSchema#dateTime">2025-11-13T06:32:55Z</dcterms:available>
    <dc:contributor>Seitz, Tim</dc:contributor>
    <foaf:homepage rdf:resource="http://localhost:8080/"/>
    <dcterms:issued>2025</dcterms:issued>
    <dc:date rdf:datatype="http://www.w3.org/2001/XMLSchema#dateTime">2025-11-13T06:32:55Z</dc:date>
    <dcterms:title>Long-time behavior of stochastic evolution equations with multiplicative rough noise</dcterms:title>
    <dspace:hasBitstream rdf:resource="https://kops.uni-konstanz.de/bitstream/123456789/75200/4/Seitz_2-1ufr4kqxtyqhm4.pdf"/>
    <dc:rights>CC0 1.0 Universal</dc:rights>
  </rdf:Description>
</rdf:RDF>
kops.date.examination2025-10-09
kops.date.yearDegreeGranted2025
kops.description.openAccessopenaccessgreen
kops.flag.knbibliographytrue
kops.identifier.nbnurn:nbn:de:bsz:352-2-1ufr4kqxtyqhm4
relation.isAuthorOfPublication7bdc8bbc-9aa5-4ae9-bc1b-cd71101df9d6
relation.isAuthorOfPublication.latestForDiscovery7bdc8bbc-9aa5-4ae9-bc1b-cd71101df9d6

Dateien

Originalbündel

Gerade angezeigt 1 - 1 von 1
Vorschaubild nicht verfügbar
Name:
Seitz_2-1ufr4kqxtyqhm4.pdf
Größe:
2.59 MB
Format:
Adobe Portable Document Format
Seitz_2-1ufr4kqxtyqhm4.pdf
Seitz_2-1ufr4kqxtyqhm4.pdfGröße: 2.59 MBDownloads: 99

Lizenzbündel

Gerade angezeigt 1 - 1 von 1
Vorschaubild nicht verfügbar
Name:
license.txt
Größe:
3.96 KB
Format:
Item-specific license agreed upon to submission
Beschreibung:
license.txt
license.txtGröße: 3.96 KBDownloads: 0

Sammlungen

Mathematik und Statistik: Publikationen