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 | |