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dc.contributor.author
Jacobe de Naurois, Ladislas
dc.contributor.author
Jentzen, Arnulf
dc.contributor.author
Welti, Timo
dc.date.accessioned
2022-01-13T18:52:30Z
dc.date.available
2021-11-17T15:02:56Z
dc.date.available
2021-11-17T15:06:47Z
dc.date.available
2022-01-13T18:52:30Z
dc.date.issued
2021-12
dc.identifier.issn
0095-4616
dc.identifier.issn
1432-0606
dc.identifier.other
10.1007/s00245-020-09744-6
en_US
dc.identifier.uri
http://hdl.handle.net/20.500.11850/515653
dc.identifier.doi
10.3929/ethz-b-000515653
dc.description.abstract
Stochastic wave equations appear in several models for evolutionary processes subject to random forces, such as the motion of a strand of DNA in a liquid or heat flow around a ring. Semilinear stochastic wave equations can typically not be solved explicitly, but the literature contains a number of results which show that numerical approximation processes converge with suitable rates of convergence to solutions of such equations. In the case of approximation results for strong convergence rates, semilinear stochastic wave equations with both additive or multiplicative noise have been considered in the literature. In contrast, the existing approximation results for weak convergence rates assume that the diffusion coefficient of the considered semilinear stochastic wave equation is constant, that is, it is assumed that the considered wave equation is driven by additive noise, and no approximation results for multiplicative noise are known. The purpose of this work is to close this gap and to establish essentially sharp weak convergence rates for spatial spectral Galerkin approximations of semilinear stochastic wave equations with multiplicative noise. In particular, our weak convergence result establishes as a special case essentially sharp weak convergence rates for the continuous version of the hyperbolic Anderson model. Our method of proof makes use of the Kolmogorov equation and the Hölder-inequality for Schatten norms.
en_US
dc.format
application/pdf
en_US
dc.language.iso
en
en_US
dc.publisher
Springer
en_US
dc.rights.uri
http://creativecommons.org/licenses/by/4.0/
dc.subject
weak convergence
en_US
dc.subject
stochastic wave equations
en_US
dc.subject
multiplicative noise
en_US
dc.subject
hyperbolic Anderson model
en_US
dc.subject
spatial approximation
en_US
dc.title
Weak Convergence Rates for Spatial Spectral Galerkin Approximations of Semilinear Stochastic Wave Equations with Multiplicative Noise
en_US
dc.type
Journal Article
dc.rights.license
Creative Commons Attribution 4.0 International
dc.date.published
2021-11-06
ethz.journal.title
Applied Mathematics & Optimization
ethz.journal.volume
84
en_US
ethz.journal.issue
2
en_US
ethz.journal.abbreviated
Appl Math Optim
ethz.pages.start
1187
en_US
ethz.pages.end
1217
en_US
ethz.version.deposit
publishedVersion
en_US
ethz.grant
Mild stochastic calculus and numerical approximations for nonlinear stochastic evolution equations with Levy noise
en_US
ethz.grant
Numerical approximations of nonlinear stochastic ordinary and partial differential equations
en_US
ethz.identifier.wos
ethz.identifier.scopus
ethz.publication.place
New York, NY
en_US
ethz.publication.status
published
en_US
ethz.leitzahl
ETH Zürich::00002 - ETH Zürich::00012 - Lehre und Forschung::00007 - Departemente::02000 - Dep. Mathematik / Dep. of Mathematics::02501 - Seminar für Angewandte Mathematik / Seminar for Applied Mathematics
en_US
ethz.leitzahl.certified
ETH Zürich::00002 - ETH Zürich::00012 - Lehre und Forschung::00007 - Departemente::02000 - Dep. Mathematik / Dep. of Mathematics::02501 - Seminar für Angewandte Mathematik / Seminar for Applied Mathematics
en_US
ethz.grant.agreementno
ETH-47 15-2
ethz.grant.agreementno
156603
ethz.grant.fundername
ETHZ
ethz.grant.fundername
SNF
ethz.grant.funderDoi
10.13039/501100003006
ethz.grant.funderDoi
10.13039/501100001711
ethz.grant.program
ETH Grants
ethz.grant.program
Projektförderung in Mathematik, Natur- und Ingenieurwissenschaften (Abteilung II)
ethz.date.deposited
2021-11-17T15:03:02Z
ethz.source
FORM
ethz.eth
yes
en_US
ethz.availability
Open access
en_US
ethz.rosetta.installDate
2022-01-13T18:52:36Z
ethz.rosetta.lastUpdated
2022-03-29T17:35:52Z
ethz.rosetta.versionExported
true
ethz.COinS
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