On a class of models of stochastic geometry constructed by random measures


Schlather, Martin


Document Type: Article
Year of publication: 2000
The title of a journal, publication series: Mathematische Nachrichten
Volume: 213
Issue number: 1
Page range: 114-154
Place of publication: Weinheim
Publishing house: Wiley-VCH
ISSN: 0025-584x
Publication language: English
Institution: School of Business Informatics and Mathematics > Mathematische Statistik (Schlather 2012-)
Subject: 510 Mathematics
Keywords (English): Measurability, σ-finite metrizable space, moment measure, Palm distribution, Poisson process, random measure, Slivnyak's theorem, stationarity
Abstract: This article presents a class of models in stochastic geometry that are constructed by random measures. This class includes well-known point processes such as Matérn's hard-core processes, the tangent point process of the Boolean model, and the point process of vertices of the Poisson Voronoi tessellation. Sufficient conditions for measurability, stationarity and isotropy of the processes of this class are given, as well as formulae for the intensity measure. Furthermore, a property of the Palm distributions can be interpreted as a generalization of Slivnyak's theorem.

Dieser Datensatz wurde nicht während einer Tätigkeit an der Universität Mannheim veröffentlicht, dies ist eine Externe Publikation.




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Schlather, Martin (2000) On a class of models of stochastic geometry constructed by random measures. Mathematische Nachrichten Weinheim 213 1 114-154 [Article]


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