Markov properties of cluster processes
UNSPECIFIED (1996) Markov properties of cluster processes. ADVANCES IN APPLIED PROBABILITY, 28 (2). pp. 346-355. ISSN 0001-8678Full text not available from this repository.
We show that a Poisson cluster point process is a nearest-neighbour Markov point process  if the clusters have uniformly bounded diameter. It is typically not a finite-range Markov point process in the sense of Ripley and Kelly . 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|
|Number of Pages:||10|
|Page Range:||pp. 346-355|
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