<div class="csl-bib-body">
<div class="csl-entry">Tempelmayr, M. (2020). <i>Sharp laplace asymptotics in infinite dimensions</i> [Diploma Thesis, Technische Universität Wien]. reposiTUm. https://doi.org/10.34726/hss.2020.75365</div>
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dc.identifier.uri
https://doi.org/10.34726/hss.2020.75365
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dc.identifier.uri
http://hdl.handle.net/20.500.12708/1454
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dc.description
Abweichender Titel nach Übersetzung der Verfasserin/des Verfassers
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dc.description.abstract
In this thesis we study the sharp asymptotic behavior of perturbations of Gaussian measures on infinite dimensional spaces. We first introduce Gaussian measures on fractional Sobolev spaces over the d-dimensional torus. Depending on the space dimension d, these spaces are spaces of functions or distributions. We then construct some perturbations of Gaussian measures for d=1,2. In the case of d=1, the perturbation is constructed using the Sobolev embedding. For d=2, problems arise since the measure we are interested in can only be defined on spaces of distributions. We remedy this by what is called renormalization procedure in literature. Key steps are the hypercontractivity estimate for the Ornstein-Uhlenbeck semigroup and Nelson's estimate. We finally determine the sharp asymptotic behavior of the perturbations constructed.
en
dc.language
English
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dc.language.iso
en
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dc.rights.uri
http://rightsstatements.org/vocab/InC/1.0/
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dc.subject
Laplace Asymptotik
de
dc.subject
Gaussmaße
de
dc.subject
Renormierung
de
dc.subject
Stochastische partielle Differentialgleichungen
de
dc.subject
Laplace asymptotics
en
dc.subject
Gaussian measures
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dc.subject
renormalization
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dc.subject
stochastic partial differential equations
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dc.title
Sharp laplace asymptotics in infinite dimensions
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dc.title.alternative
Scharfe Laplace Asymptotik in unendlicher Dimension
de
dc.type
Thesis
en
dc.type
Hochschulschrift
de
dc.rights.license
In Copyright
en
dc.rights.license
Urheberrechtsschutz
de
dc.identifier.doi
10.34726/hss.2020.75365
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dc.contributor.affiliation
TU Wien, Österreich
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dc.rights.holder
Markus Tempelmayr
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dc.publisher.place
Wien
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tuw.version
vor
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tuw.thesisinformation
Technische Universität Wien
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dc.contributor.assistant
Di Gesu, Giacomo
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tuw.publication.orgunit
E105 - Institut für Stochastik und Wirtschaftsmathematik
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dc.type.qualificationlevel
Diploma
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dc.identifier.libraryid
AC15618908
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dc.description.numberOfPages
57
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dc.identifier.urn
urn:nbn:at:at-ubtuw:1-135885
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dc.thesistype
Diplomarbeit
de
dc.thesistype
Diploma Thesis
en
dc.rights.identifier
In Copyright
en
dc.rights.identifier
Urheberrechtsschutz
de
tuw.advisor.staffStatus
staff
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tuw.assistant.staffStatus
staff
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item.openaccessfulltext
Open Access
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item.openairecristype
http://purl.org/coar/resource_type/c_bdcc
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item.grantfulltext
open
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item.mimetype
application/pdf
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item.languageiso639-1
en
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item.openairetype
master thesis
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item.fulltext
with Fulltext
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item.cerifentitytype
Publications
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crisitem.author.dept
E101 - Institut für Analysis und Scientific Computing