Spatial point process models with applications to max-stable random fields

Dirrler, Martin

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URN: urn:nbn:de:bsz:180-madoc-430942
Document Type: Doctoral dissertation
Year of publication: 2017
Place of publication: Mannheim
University: Universität Mannheim
Evaluator: Schlather, Martin
Date of oral examination: 25 October 2017
Publication language: English
Institution: School of Business Informatics and Mathematics > Applied Stochastics (Schlather 2012-)
Subject: 510 Mathematics
Subject headings (SWD): Punktprozess
Keywords (English): point processes, max-stable, dependent thinning
Abstract: In Part I of this thesis, we briefly summarize some theory of point processes which is crucial for the subsequent parts. We introduce a class of spatial stochastic processes in the max-domain of attraction of familiar max-stable processes in Part II. The new class is based on Cox processes instead of Poisson processes. We show that statistical inference is possible within the given framework, at least under some reasonable restrictions. The Matérn hard-core processes are classical examples for point process models ob- tained from (marked) Poisson point processes. Points of the original Poisson process are deleted according to a dependent thinning rule, resulting in a process whose points have a prescribed hard-core distance. In Part III, we present a new model which generalizes the underlying point process, the thinning rule and the marks attached to the original process. The new model further reveals several connections to mixed moving maxima processes, e.g. a process of visible storm centres.

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