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Gamma-type results and other related properties of Poisson processes

Part of: Inference from stochastic processes Geometric probability and stochastic geometry

Published online by Cambridge University Press:  01 July 2016

Jesper Møller  and
Sergei Zuyev
Jesper Møller*
Affiliation:
Aalborg University
Sergei Zuyev*
Affiliation:
Institut National de Recherche en Informatique et en Automatique
*
∗ Postal address: Department of Mathematics and Computer Science, Aalborg University, F. Bajers Vej 7E, DK-9220 Aalborg, Denmark. email: jm@iesd.auc.dk
∗∗ Postal address: Institut National de Recherche en Informatique et en Automatique, 2004, route des Lucioles, BP 93, 06902 Sophia-Antipolis Cedex, France. email: sergei@gville.inria.fr
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Abstract

Families of Poisson processes defined on general state spaces and with the intensity measure scaled by a positive parameter are investigated. In particular, mean value relations with respect to the scale parameter are established and used to derive various Gamma-type results for certain geometric characteristics determined by finite subprocesses. In particular, we deduce Miles' complementary theorem. Applications of the results within stochastic geometry and particularly for random tessellations are discussed.

Keywords

COMPLEMENTARY THEOREMDELAUNAY TESSELLATIONGAMMA DISTRIBUTIONHYPERPLANE TESSELLATIONSPALM PROBABILITIESPOISSON FLAT PROCESSESPOISSON POINT PROCESSESSLIVNYAK'S THEOREMSTOCHASTIC GEOMETRYTESSELLATION CHARACTERISTICSVORONOI TESSELLATION

MSC classification

Primary: 60D05: Geometric probability and stochastic geometry
Secondary: 62M30: Spatial processes
Type
Stochastic Geometry and Statistical Applications
Information
Advances in Applied Probability , Volume 28 , Issue 3 , September 1996 , pp. 662 - 673
Copyright
Copyright © Applied Probability Trust 1996 

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