Characterization and construction of max-stable processes

Strokorb, Kirstin

dc.contributor.advisor	Krajina, Andrea Prof. Dr.
dc.contributor.author	Strokorb, Kirstin
dc.date.accessioned	2013-08-30T08:52:52Z
dc.date.available	2013-08-30T08:52:52Z
dc.date.issued	2013-08-30
dc.identifier.uri	http://hdl.handle.net/11858/00-1735-0000-0001-BB44-9
dc.identifier.uri	http://dx.doi.org/10.53846/goediss-4022
dc.language.iso	eng	de
dc.rights.uri	http://creativecommons.org/licenses/by-nc-nd/3.0/
dc.subject.ddc	510	de
dc.title	Characterization and construction of max-stable processes	de
dc.type	doctoralThesis	de
dc.contributor.referee	Krajina, Andrea Prof. Dr.
dc.date.examination	2013-07-02
dc.description.abstracteng	Max-stable processes provide a natural framework to model spatial extremal scenarios. Appropriate summary statistics include the extremal coefficients and the (upper) tail dependence coefficients. In this thesis, the full set of extremal coefficients of a max-stable process is captured in the so-called extremal coefficient function (ECF) and the full set of upper tail dependence coefficients in the tail correlation function (TCF). Chapter 2 deals with a complete characterization of the ECF in terms of negative definiteness. For each ECF a corresponding max-stable process is constructed, which takes an exceptional role among max-stable processes with identical ECF. This leads to sharp lower bounds for the finite dimensional distributions of arbitrary max-stable processes in terms of its ECF. Chapters 3 and 4 are concerned with the class of TCFs. Chapter 3 exhibits this class as an infinite-dimensional compact convex polytope. It is shown that the set of all TCFs (of not necessarily max-stable processes) coincides with the set of TCFs stemming from max-stable processes. Chapter 4 compares the TCFs of widely used stationary max-stable processes such as Mixed Moving Maxima, Extremal Gaussian and Brown-Resnick processes. Finally, in Chapter 5, Brown-Resnick processes on the sphere and other spaces admitting a compact group action are considered and a Mixed Moving Maxima representation is derived.	de
dc.contributor.coReferee	Schaback, Robert Prof. Dr.
dc.contributor.thirdReferee	Schlather, Martin Prof. Dr.
dc.contributor.thirdReferee	Molchanov, Ilya Prof. Dr.
dc.subject.eng	extreme value theory	de
dc.subject.eng	max-stable process	de
dc.subject.eng	extremal coefficient	de
dc.subject.eng	negative definite	de
dc.subject.eng	tail correlation	de
dc.subject.eng	positive definite	de
dc.subject.eng	dependency set	de
dc.subject.eng	harmonic analysis	de
dc.subject.eng	mixed moving maxima	de
dc.subject.eng	Brown-Resnick process	de
dc.subject.eng	extremal Gaussian process	de
dc.subject.eng	tail dependence	de
dc.identifier.urn	urn:nbn:de:gbv:7-11858/00-1735-0000-0001-BB44-9-4
dc.affiliation.institute	Fakultät für Mathematik und Informatik	de
dc.subject.gokfull	Mathematics (PPN61756535X)	de
dc.identifier.ppn	766639878

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