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On a Class of Models of Stochastic Geometry Constructed by Random Measures
Author(s) -
Schlather Martin
Publication year - 2000
Publication title -
mathematische nachrichten
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.913
H-Index - 50
eISSN - 1522-2616
pISSN - 0025-584X
DOI - 10.1002/(sici)1522-2616(200005)213:1<141::aid-mana141>3.0.co;2-m
Subject(s) - mathematics , point process , boolean model , stochastic geometry , poisson point process , class (philosophy) , generalization , tangent , measure (data warehouse) , point (geometry) , isotropy , voronoi diagram , stochastic process , geometry , mathematical analysis , discrete mathematics , statistics , computer science , physics , quantum mechanics , database , artificial intelligence
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.