Berry-Esseen bounds and Cramér-type large deviations for the volume distribution of Poisson cylinder processes

DOI10.1007/s10986-009-9061-9zbMath1186.60017OpenAlexW2008826539MaRDI QIDQ847907

Lothar Heinrich, Malte Spiess

Publication date: 19 February 2010

Published in: Lithuanian Mathematical Journal (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1007/s10986-009-9061-9

zbMATH Keywords

volume fractioncentral limit theoremhigher-order (mixed) cumulantsmoment- and cumulant-generating functionrandom (closed) setstationary 0-1-random field

Mathematics Subject Classification ID

Geometric probability and stochastic geometry (60D05) Central limit and other weak theorems (60F05) Large deviations (60F10) Point processes (e.g., Poisson, Cox, Hawkes processes) (60G55)

Related Items

The method of cumulants for the normal approximation, Berry-Esseen bounds and Cramér-type large deviations for the volume distribution of Poisson cylinder processes, Variance asymptotics and central limit theory for geometric functionals of Poisson cylinder processes, Mixing properties of stationary Poisson cylinder models, Variance asymptotics for the area of planar cylinder processes generated by Brillinger-mixing point processes, Moderate deviations for stabilizing functionals in geometric probability, Concentration inequalities for functionals of Poisson cylinder processes, Central Limit Theorems for Volume and Surface Content of Stationary Poisson Cylinder Processes in Expanding Domains, The volume of simplices in high-dimensional Poisson-Delaunay tessellations, Second-order properties and central limit theorems for geometric functionals of Boolean models

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