Markov properties of cluster processes

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

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    28 Citations (Scopus)

    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.
    Original languageEnglish
    Pages (from-to)346-355
    Number of pages10
    JournalAdvances in Applied Probability
    Volume28
    Issue number2
    DOIs
    Publication statusPublished - 1996

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  • Cite this

    Baddeley, A. J., Lieshout, van, M. N. M., & Møller, J. (1996). Markov properties of cluster processes. Advances in Applied Probability, 28(2), 346-355. https://doi.org/10.2307/1428060