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Publisher DOI: 10.1214/22-EJP805
Title: Variance asymptotics and central limit theory for geometric functionals of Poisson cylinder processes
Language: English
Authors: Betken, Carina 
Schulte, Matthias 
Thäle, Christoph 
Keywords: Berry-Esseen bound; central limit theorem; geometric functional; intrinsic volume; multivariate central limit theorem; Poisson cylinder process; second-order Poincaré inequality; stochastic geometry; variance asymptotics
Issue Date: Jun-2022
Publisher: Univ. of Washington, Mathematics Dep.
Source: Electronic Journal of Probability 27: 79 (2022)
Abstract (english): 
This paper deals with the union set of a stationary Poisson process of cylinders in Rn having an (n − m)-dimensional base and an m-dimensional direction space, where m ∈ 0, 1, …, n − 1 and n ≥ 2. The concept simultaneously generalises those of a Boolean model and a Poisson hyperplane or m-flat process. Under very general conditions on the typical cylinder base a Berry-Esseen bound for the volume of the union set within a sequence of growing test sets is derived. Assuming convexity of the cylinder bases and of the window a similar result is shown for a broad class of geometric functionals, including the intrinsic volumes. In this context the asymptotic variance constant is analysed in detail, which in contrast to the Boolean model leads to a new degeneracy phenomenon. A quantitative central limit theory is developed in a multivariate set-up as well.
DOI: 10.15480/882.4531
ISSN: 1083-6489
Journal: Electronic journal of probability 
Institute: Mathematik E-10 
Document Type: Article
License: CC BY 4.0 (Attribution) CC BY 4.0 (Attribution)
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