UNSPECIFIED (1996) Markov properties of cluster processes. ADVANCES IN APPLIED PROBABILITY, 28 (2). pp. 346-355. ISSN 0001-8678

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Abstract

We show that a Poisson cluster point process is a nearest-neighbour Markov point process [2] if the clusters have uniformly bounded diameter. It is typically not a finite-range Markov point process in the sense of Ripley and Kelly [12]. Furthermore, when the parent Poisson process is replaced by a Markov or nearest-neighbour Markov point process, the resulting cluster process is also nearest-neighbour Markov, provided all clusters are non-empty. in particular, the nearest-neighbour Markov property is preserved when points of the process are independently randomly translated, but not when they are randomly thinned.

Item Type:	Journal Article
Subjects:	Q Science > QA Mathematics
Journal or Publication Title:	ADVANCES IN APPLIED PROBABILITY
Publisher:	APPLIED PROBABILITY TRUST
ISSN:	0001-8678
Date:	June 1996
Volume:	28
Number:	2
Number of Pages:	10
Page Range:	pp. 346-355
Publication Status:	Published
URI:	http://wrap.warwick.ac.uk/id/eprint/18757

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