Markov properties of cluster processes

Adrian Baddeley, M.N.M. Van Lieshout, J. Moller

    Research output: Contribution to journalArticle

    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
    JournalAdvances in Applied Probability
    Volume28
    DOIs
    Publication statusPublished - 1996

    Fingerprint Dive into the research topics of 'Markov properties of cluster processes'. Together they form a unique fingerprint.

    Cite this