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Multivariate Mixed Poisson Processes / Multivariate gemischte Poisson-Prozesse

Multivariate mixed Poisson processes are special multivariate counting processes whose coordinates are, in general, dependent. The first part of this thesis is devoted to properties which multivariate counting processes may possess. Such properties are, for example, the Markov property, the multinomial property and regularity. With regard to regularity we study the properties of transition probabilities and intensities. The second part of this thesis restricts the class of all multivariate counting processes by additional assumptions leading to different types of multivariate mixed Poisson processes which, however, are connected with each other. Using a multivariate version of the Bernstein-Widder theorem, it is shown that multivariate mixed Poisson processes are characterized by the multinomial property. Furthermore, regularity of multivariate mixed Poisson processes and properties of their moments are studied in detail. Throughout this thesis, two types of stability of properties of multivariate counting processes are studied: It is shown that most properties of a multivariate counting process are stable under certain linear transformations including the selection of single coordinates and summation of all coordinates. It is also shown that the different types of multivariate mixed Poisson processes under consideration are in a certain sense stable in time.

Identiferoai:union.ndltd.org:DRESDEN/oai:qucosa.de:swb:14-1134744627176-09576
Date19 November 2005
CreatorsZocher, Mathias
ContributorsTechnische Universität Dresden, Mathematik und Naturwissenschaften, Mathematik, Institut für Mathematische Stochastik, Prof. Dr. Klaus D. Schmidt, Prof. Dr. Gerold Alsmeyer, Prof. Dr. Rolf Kühne, Prof. Dr. Klaus D. Schmidt
PublisherSaechsische Landesbibliothek- Staats- und Universitaetsbibliothek Dresden
Source SetsHochschulschriftenserver (HSSS) der SLUB Dresden
LanguageEnglish
Detected LanguageEnglish
Typedoc-type:doctoralThesis
Formatapplication/pdf

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