Markov properties of cluster processes

A.J. Baddeley, M.N.M. Lieshout, van, J. Møller

    Research output: Contribution to journalArticleAcademicpeer-review

    29 Citations (Scopus)


    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.
    Original languageEnglish
    Pages (from-to)346-355
    Number of pages10
    JournalAdvances in Applied Probability
    Issue number2
    Publication statusPublished - 1996


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