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Markov properties of cluster processes
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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 | ||||
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Subjects: | Q Science > QA Mathematics | ||||
Journal or Publication Title: | ADVANCES IN APPLIED PROBABILITY | ||||
Publisher: | APPLIED PROBABILITY TRUST | ||||
ISSN: | 0001-8678 | ||||
Official Date: | June 1996 | ||||
Dates: |
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Volume: | 28 | ||||
Number: | 2 | ||||
Number of Pages: | 10 | ||||
Page Range: | pp. 346-355 | ||||
Publication Status: | Published |
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