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• W2073451260 abstract "Summary. For stationary POISSON cluster processes (PCP's) Ø on R the limit behaviour, as v(D) → ∞, of the quantity documentclass{article}pagestyle{empty}begin{document}$ left({vleft(D right)} right)^{ - 1} sumlimits_{xvarepsilon D:phi left({left{ x right}} right) = 1} {chi left({x,r} right)} $end{document}, where χ(x, r) = 1, if Ø(b(x, r)) = 1, and χ(x, r) = 0 otherwise, is studied. A central limit theorem for fixed r > 0 and the weak convergence of the normalized and centred empirical process on [0, R] to a continuous GAUSSian process are proved. Lower and upper bounds for the nearest neighbour distance function P1({φ:Y(b(0,r))≧1}) of a stationary PCP are given. Moreover, a representation of higher order Palm distributions of PCP's and a central limit theorem for m-dependent random fields with unbounded m are obtained. Both these auxiliary results seems to be of own interest." @default.
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• W2073451260 date "1988-01-01" @default.
• W2073451260 modified "2023-09-23" @default.
• W2073451260 title "Asymptotic Behaviour of an Empirical Nearest-Neighbour Distance Function for Stationary Poisson Cluster Processes" @default.
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• W2073451260 doi "https://doi.org/10.1002/mana.19881360109" @default.
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