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On a Class of Models of Stochastic Geometry Constructed by Random Measures

✍ Scribed by Martin Schlather

Publisher: John Wiley and Sons
Year: 2000
Tongue: English
Weight: 319 KB
Volume: 213
Category: Article
ISSN: 0025-584X
DOI: 10.1002/(sici)1522-2616(200005)213:1<141::aid-mana141>3.0.co;2-m

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✦ Synopsis

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.

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