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Markov interacting component processes

Part of: Stochastic processes Geometric probability and stochastic geometry

Published online by Cambridge University Press:  19 February 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

A generalization of Markov point processes is introduced in which interactions occur between connected components of the point pattern. A version of the Hammersley-Clifford characterization theorem is proved which states that a point process is a Markov interacting component process if and only if its density function is a product of interaction terms associated with cliques of connected components. Integrability and superpositional properties of the processes are shown and a pairwise interaction example is used for detailed exploration.

Keywords

Markov point processesconnected componentssuperpositionspatial statisticsclusteringconditional intensity

MSC classification

Primary: 60G55: Point processes
Secondary: 60D05: Geometric probability and stochastic geometry
Type
Stochastic Geometry and Statistical Applications
Information
Advances in Applied Probability , Volume 32 , Issue 3 , September 2000 , pp. 597 - 619
Copyright
Copyright © Applied Probability Trust 2000 

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