A note on expansion for functionals of spatial marked point processes

DOI10.1016/S0167-7152(97)00076-XzbMath0897.60050MaRDI QIDQ1382228

Volker Schmidt, Ely Merzbach, Bartlomiej Blaszczyszyn

Publication date: 25 March 1998

Published in: Statistics \& Probability Letters (Search for Journal in Brave)

zbMATH Keywords

moment measurefactorial expansionclump sizeprobability generating functionalspatial marked point process

Mathematics Subject Classification ID

Geometric probability and stochastic geometry (60D05) Point processes (e.g., Poisson, Cox, Hawkes processes) (60G55)

Related Items (5)

A functional central limit theorem for the empirical Ripley's \(K\)-function ⋮ Nonparametric estimation for compound Poisson process via variational analysis on measures ⋮ Decorrelation of a class of Gibbs particle processes and asymptotic properties of U-statistics ⋮ Central limit theorem for exponentially quasi-local statistics of spin models on Cayley graphs ⋮ Differentiability of functionals of Poisson processes via coupling. With applications to queueing theory

Cites Work

• Point processes indexed by directed sets
• An introduction to the theory of point processes
• Factorial moment espansion for stochastic systems
• Taylor series expansions for Poisson-driven (max,+)-linear systems
• Taylor-series expansion for multivariate characteristics of classical risk processes
• Open Queueing Systems in Light Traffic
• Light-traffic approximations for Markov-modulated multi-server queues
• Expansions for Markov-modulated systems and approximations of ruin probability
• Virtual customers in sensitivity and light traffic analysis via Campbell's formula for point processes
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