Please use this identifier to cite or link to this item:
https://doi.org/10.15480/882.4531
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. |
URI: | http://hdl.handle.net/11420/13380 | DOI: | 10.15480/882.4531 | ISSN: | 1083-6489 | Journal: | Electronic journal of probability | Institute: | Mathematik E-10 | Document Type: | Article | License: | ![]() |
Appears in Collections: | Publications with fulltext |
Files in This Item:
File | Description | Size | Format | |
---|---|---|---|---|
22-EJP805.pdf | Verlags-PDF | 1,48 MB | Adobe PDF | View/Open![]() |
Note about this record
Cite this record
Export
This item is licensed under a Creative Commons License