Central Limit Theorems for Volume and Surface Content of Stationary Poisson Cylinder Processes in Expanding Domains

DOI10.1239/aap/1370870120zbMath1282.60012OpenAlexW2058088351MaRDI QIDQ2837749

Malte Spiess, Lothar Heinrich

Publication date: 11 July 2013

Published in: Advances in Applied Probability (Search for Journal in Brave)

Full work available at URL: https://projecteuclid.org/euclid.aap/1370870120

zbMATH Keywords

volume fractionasymptotic variancelong-range dependenceindependently marked Poisson processdirection spacemoment convergence theoremhigher-order (mixed) cumulanttruncated typical cylinder

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 (10)

Second-order characteristics of the edge system of random tessellations and the PPI value of foams ⋮ The method of cumulants for the normal approximation ⋮ Multivariate Poisson distributions associated with Boolean models ⋮ Variance asymptotics and central limit theory for geometric functionals of Poisson cylinder processes ⋮ Hyperuniform states of matter ⋮ Some inequalities for chord power integrals of parallelotopes ⋮ Mixing properties of stationary Poisson cylinder models ⋮ Variance asymptotics for the area of planar cylinder processes generated by Brillinger-mixing point processes ⋮ Concentration inequalities for functionals of Poisson cylinder processes ⋮ Second-order properties and central limit theorems for geometric functionals of Boolean models

Cites Work

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• Anisotropic Poisson processes of cylinders
• Geometric inequalities for Poisson processes of convex bodies and cylinders
• Berry-Esseen bounds and Cramér-type large deviations for the volume distribution of Poisson cylinder processes
• Central limit theorems for Poisson hyperplane tessellations
• Mixed measures of convex cylinders and quermass densities of Boolean models
• Point processes of cylinders, particles and flats
• Large deviations of the empirical volume fraction for stationary Poisson grain models
• On a Method of Calculation of Semi-Invariants
• Stochastic and Integral Geometry
• Normal convergence of multidimensional shot noise and rates of this convergence
• Electromagnetic wave propagation and inequalities for moments of chord lengths
• Statistics of the Boolean model: from the estimation of means to the estimation of distributions
• Central limit theorem for a class of random measures associated with germ-grain models
• An Introduction to the Theory of Point Processes
• Theory of Random Sets
• An Introduction to the Theory of Point Processes
• On the second derivative of the spherical contact distribution function of smooth grain models

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