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dc.contributor.author
Barth, Andrea
dc.contributor.author
Lang, Annika
dc.date.accessioned
2017-06-09T16:50:31Z
dc.date.available
2017-06-09T16:50:31Z
dc.date.issued
2011-03
dc.identifier.uri
http://hdl.handle.net/20.500.11850/40076
dc.description.abstract
In this paper $L^p$ convergence and almost sure convergence of the Milstein approximation of a partial differential equation of advection-diffusion type driven by a multiplicative continuous martingale is proved. The (semidiscrete) approximation in space is a projection onto a finite dimensional subspace. The space approximation considered has to have an order of convergence fitting to the order of convergence of the Milstein approximation and the regularity of the solution. The approximation of the driving noise process is realized by the truncation of the Karhunen-Loève expansion according to the overall order of convergence. Convergence in $L^p$ and almost sure convergence of the semidiscrete approximation as well as of the fully discrete approximation are provided.
dc.language.iso
en
dc.publisher
Seminar für Angewandte Mathematik, ETH
dc.subject
Stochastic partial differential equation
dc.subject
Lp convergence
dc.subject
Almost sure convergence
dc.subject
Milstein scheme
dc.subject
Galerkin method
dc.subject
Finite Element method
dc.subject
Crank-Nicolson scheme
dc.title
Lp and almost sure convergence of a Milstein scheme for stochastic partial differential equations
dc.type
Report
ethz.journal.title
Research reports
ethz.journal.issue
2011/15
ethz.journal.abbreviated
Res. rep.- Natl. Geogr. Soc.
ethz.size
27
ethz.notes
.
ethz.publication.place
Zürich
ethz.publication.status
unpublished
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::03435 - Schwab, Christoph / Schwab, Christoph
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::03435 - Schwab, Christoph / Schwab, Christoph
ethz.identifier.url
http://www.sam.math.ethz.ch/reports/2011/15
ethz.date.deposited
2017-06-09T16:50:56Z
ethz.source
ECIT
ethz.identifier.importid
imp59364e8fa502852310
ethz.ecitpid
pub:67195
ethz.eth
yes
ethz.availability
Metadata only
ethz.rosetta.installDate
2017-07-14T12:06:03Z
ethz.rosetta.lastUpdated
2018-10-01T14:01:44Z
ethz.rosetta.versionExported
true
ethz.COinS
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