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On connected component Markov point processes

Part of: Stochastic processes Geometric probability and stochastic geometry

Published online by Cambridge University Press:  01 July 2016

Y. C. Chin  and
A. J. Baddeley
Y. C. Chin*
Affiliation:
The University of Western Australia
A. J. Baddeley*
Affiliation:
The University of Western Australia
*
∗ Postal address: Department of Mathematics and Statistics, The University of Western Australia, Nedlands, WA 6907, Australia.
∗ Postal address: Department of Mathematics and Statistics, The University of Western Australia, Nedlands, WA 6907, Australia.
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Abstract

We note some interesting properties of the class of point processes which are Markov with respect to the ‘connected component’ relation. Results in the literature imply that this class is closed under random translation and independent cluster generation with almost surely non-empty clusters. We further prove that it is closed under superposition. A wide range of examples is also given.

Keywords

Cluster processescontinuum random cluster modelsuperposition of point processesnearest neighbour Markov point processes

MSC classification

Primary: 60G55: Point processes
Secondary: 60D05: Geometric probability and stochastic geometry

Information

Type
Stochastic Geometry and Statistical Applications
Information
Advances in Applied Probability , Volume 31 , Issue 2 , June 1999 , pp. 279 - 282
Copyright
Copyright © Applied Probability Trust 1999 

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References

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