Please use this identifier to cite or link to this item: https://doi.org/10.15480/882.4531
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dc.contributor.authorBetken, Carina-
dc.contributor.authorSchulte, Matthias-
dc.contributor.authorThäle, Christoph-
dc.date.accessioned2022-08-04T08:54:56Z-
dc.date.available2022-08-04T08:54:56Z-
dc.date.issued2022-06-
dc.identifier.citationElectronic Journal of Probability 27: 79, 1-47 (2022)de_DE
dc.identifier.issn1083-6489de_DE
dc.identifier.urihttp://hdl.handle.net/11420/13380-
dc.description.abstractThis 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.en
dc.language.isoende_DE
dc.publisherUniv. of Washington, Mathematics Dep.de_DE
dc.relation.ispartofElectronic journal of probabilityde_DE
dc.rights.urihttps://creativecommons.org/licenses/by/4.0/de_DE
dc.subjectBerry-Esseen boundde_DE
dc.subjectcentral limit theoremde_DE
dc.subjectgeometric functionalde_DE
dc.subjectintrinsic volumede_DE
dc.subjectmultivariate central limit theoremde_DE
dc.subjectPoisson cylinder processde_DE
dc.subjectsecond-order Poincaré inequalityde_DE
dc.subjectstochastic geometryde_DE
dc.subjectvariance asymptoticsde_DE
dc.subject.ddc600: Technikde_DE
dc.titleVariance asymptotics and central limit theory for geometric functionals of Poisson cylinder processesde_DE
dc.typeArticlede_DE
dc.identifier.doi10.15480/882.4531-
dc.type.diniarticle-
dcterms.DCMITypeText-
tuhh.identifier.urnurn:nbn:de:gbv:830-882.0193891-
tuhh.oai.showtruede_DE
tuhh.abstract.englishThis 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.de_DE
tuhh.publisher.doi10.1214/22-EJP805-
tuhh.publication.instituteMathematik E-10de_DE
tuhh.identifier.doi10.15480/882.4531-
tuhh.type.opus(wissenschaftlicher) Artikel-
dc.type.driverarticle-
dc.type.casraiJournal Article-
tuhh.container.volume27de_DE
tuhh.container.startpage1de_DE
tuhh.container.endpage47de_DE
dc.rights.nationallicensefalsede_DE
dc.identifier.scopus2-s2.0-85132893311de_DE
tuhh.container.articlenumber79de_DE
local.status.inpressfalsede_DE
local.type.versionpublishedVersionde_DE
datacite.resourceTypeArticle-
datacite.resourceTypeGeneralJournalArticle-
item.grantfulltextopen-
item.openairecristypehttp://purl.org/coar/resource_type/c_6501-
item.creatorGNDBetken, Carina-
item.creatorGNDSchulte, Matthias-
item.creatorGNDThäle, Christoph-
item.openairetypeArticle-
item.fulltextWith Fulltext-
item.cerifentitytypePublications-
item.creatorOrcidBetken, Carina-
item.creatorOrcidSchulte, Matthias-
item.creatorOrcidThäle, Christoph-
item.languageiso639-1en-
item.mappedtypeArticle-
crisitem.author.deptMathematik E-10-
crisitem.author.parentorgStudiendekanat Elektrotechnik, Informatik und Mathematik-
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