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• W3211598722 abstract "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." @default.
• W3211598722 created "2021-11-22" @default.
• W3211598722 creator A5013850827 @default.
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• W3211598722 date "2022-01-01" @default.
• W3211598722 modified "2023-09-26" @default.
• W3211598722 title "Variance asymptotics and central limit theory for geometric functionals of Poisson cylinder processes" @default.
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• W3211598722 doi "https://doi.org/10.1214/22-ejp805" @default.
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