TY - JOUR
T1 - Markov properties of cluster processes
AU - Baddeley, Adrian
AU - Van Lieshout, M.N.M.
AU - Moller, J.
PY - 1996
Y1 - 1996
N2 - 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.
AB - 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.
U2 - 10.2307/1428060
DO - 10.2307/1428060
M3 - Article
VL - 28
SP - 346
EP - 355
JO - Advances in Applied Probability (SGSA)
JF - Advances in Applied Probability (SGSA)
SN - 0001-8678
ER -