Brown-Resnick Processes: Analysis, Inference and Generalizations

Engelke, Sebastian

dc.contributor.advisor	Schlather, Martin Prof. Dr.	de
dc.contributor.author	Engelke, Sebastian	de
dc.date.accessioned	2013-01-25T10:48:13Z	de
dc.date.available	2013-01-30T23:51:00Z	de
dc.date.issued	2013-01-25	de
dc.identifier.uri	http://hdl.handle.net/11858/00-1735-0000-000D-F1B3-2	de
dc.identifier.uri	http://dx.doi.org/10.53846/goediss-3370
dc.language.iso	eng	de
dc.publisher	Niedersächsische Staats- und Universitätsbibliothek Göttingen	de
dc.rights.uri	http://creativecommons.org/licenses/by-nc-nd/3.0/
dc.subject.ddc	510	de
dc.title	Brown-Resnick Processes: Analysis, Inference and Generalizations	de
dc.type	doctoralThesis	de
dc.contributor.referee	Schlather, Martin Prof. Dr.	de
dc.date.examination	2012-12-14	de
dc.description.abstracteng	This thesis deals with the analysis, inference and further generalizations of a rich and flexible class of max-stable random fields, the so-called Brown-Resnick processes. The first chapter gives the explicit distribution of the shape functions in the mixed moving maxima representation of the original Brown-Resnick process based on Brownian motions. The result is particularly useful for a fast simulation method. In chapter 2, a multivariate peaks-over-threshold approach for parameter estimation of Hüsler-Reiss distributions, a popular model in multivariate extreme value theory, is presented. As Hüsler-Reiss distributions constitute the finite dimensional margins of Brown-Resnick processes based on Gaussian random fields, the estimators directly enable statistical inference for this class of max-stable processes. As an application, a non-isotropic Brown-Resnick process is fitted to the extremes of 12-year data of daily wind speed measurements. Chapter 3 is concerned with the definition of Brown-Resnick processes based on Lévy processes on the whole real line. Amongst others, it is shown that these Lévy-Brown-Resnick processes naturally arise as limits of maxima of stationary stable Ornstein-Uhlenbeck processes. The last chapter is devoted to the study of maxima of d-variate Gaussian triangular arrays, where in each row the random vectors are assumed to be independent, but not necessarily identically distributed. The row-wise maxima converge to a new class of multivariate max-stable distributions, which can be seen as max-mixtures of Hüsler-Reiss distributions.	de
dc.contributor.coReferee	Sturm, Anja Prof. Dr.	de
dc.contributor.thirdReferee	Stoev, Stilian Prof. Dr.	de
dc.subject.eng	Brown-Resnick processes	de
dc.subject.eng	max-stable processes	de
dc.subject.eng	Gaussian random fields	de
dc.subject.eng	extreme value theory	de
dc.subject.eng	mixed moving maxima	de
dc.subject.eng	extreme value statistics	de
dc.subject.eng	Hüsler-Reiss distributions	de
dc.subject.eng	Lévy processes	de
dc.subject.eng	triangular arrays	de
dc.subject.eng	extremal correlation functions	de
dc.subject.eng	max-limit theorems	de
dc.subject.eng	Poisson point processes	de
dc.identifier.urn	urn:nbn:de:gbv:7-11858/00-1735-0000-000D-F1B3-2-6	de
dc.affiliation.institute	Fakultät für Mathematik und Informatik	de
dc.subject.gokfull	Mathematics (PPN61756535X)	de
dc.identifier.ppn	737346310	de

Dateien

Name:Dissertation_Engelke.pdf

Größe:2.327Mb

Format:PDF

Beschreibung:Dissertation

Öffnen

Name:: Dissertation_Engelke.pdf
Größe:: 2.327Mb
Format:: PDF
Beschreibung:: Dissertation

Öffnen

Das Dokument erscheint in:

Fakultät für Mathematik und Informatik (inkl. GAUSS) [518]

Zur Kurzanzeige