Gaussian loop- and Pólya processes : a point process approach

This thesis considers on the one hand the construction of point processes via conditional intensities, motivated by the partial Integration of the Campbell measure of a point process. Under certain assumptions on the intensity the existence of such a point process is shown. A fundamental example turns out to be the Pólya sum process, whose conditional intensity is a generalisation of the Pólya urn dynamics. A Cox process representation for that point process is shown. A further process considered is a Poisson process of Gaussian loops, which represents a noninteracting particle system derived from the discussion of indistinguishable particles. Both processes are used to define particle systems locally, for which thermodynamic limits are determined.

Level thesis:degree_level

thesis.doctoral

Grantor dc:publisher

Universität Potsdam

Year

2009

Author dc:creator

• Rafler, Mathias

Contributors dc:contributor

• Roelly, Sylvie

• Punktprozesse
• partielle Integration
• Gaußsche Loopprozess
• Papangelou-Prozess
• Polyascher Prozess
• Point Processes
• Partial Integration
• Gaussian Loop Processes
• Papangelou Process
• Polya Process

Statement dc:rights

• Creative Commons - Namensnennung, Nicht kommerziell, Weitergabe zu gleichen Bedingungen 3.0 Deutschland

Repository record source_url

https://publishup.uni-potsdam.de/frontdoor/index/index/docId/3841

OAI identifier oai:identifier

oai:kobv.de-opus4-uni-potsdam:3841