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Characterization and construction of max-stable processes

dc.contributor.advisorKrajina, Andrea Prof. Dr.
dc.contributor.authorStrokorb, Kirstin
dc.titleCharacterization and construction of max-stable processesde
dc.contributor.refereeKrajina, Andrea Prof. Dr.
dc.description.abstractengMax-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
dc.contributor.coRefereeSchaback, Robert Prof. Dr.
dc.contributor.thirdRefereeSchlather, Martin Prof. Dr.
dc.contributor.thirdRefereeMolchanov, Ilya Prof. Dr.
dc.subject.engextreme value theoryde
dc.subject.engmax-stable processde
dc.subject.engextremal coefficientde
dc.subject.engnegative definitede
dc.subject.engtail correlationde
dc.subject.engpositive definitede
dc.subject.engdependency setde
dc.subject.engharmonic analysisde
dc.subject.engmixed moving maximade
dc.subject.engBrown-Resnick processde
dc.subject.engextremal Gaussian processde
dc.subject.engtail dependencede
dc.affiliation.instituteFakultät für Mathematik und Informatikde
dc.subject.gokfullMathematics (PPN61756535X)de

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