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AuthorSchmidt, Hendrikdc.contributor.author
Date of accession2016-03-14T13:38:56Zdc.date.accessioned
Available in OPARU since2016-03-14T13:38:56Zdc.date.available
Year of creation2006dc.date.created
AbstractThis thesis arose out of a joint research project between the Department of Stochastics at the University of Ulm and France Télécom R&D Division in Paris. In particular it was stimulated by questions regarding statistical model fitting of random tessellation models to data that exhibit network structure and describe for example the infrastructure in metropolitan areas. In a first part, possible network geometry models, i.e. random tessellations, are studied along with their structural behaviour. This means in particular to analyse functionals induced by such tessellations as well as to examine their (asymptotic) distributional behaviour. Indeed, central limit theorems (CLTs) for stationary tessellation models in d-dimensional Euclidean space are derived. They show that the asymptotic distribution of (suitably centered and normalized) functionals of the tessellation itself or of some structure embedded randomly within the cells induced by the tessellation is a normal distribution. The study is based on the observation of a single realization of the underlying tessellation model through some (convex compact) sampling window and the term "asymptotic" means that this sampling window is assumed to expand uniformly but unboundedly in all directions. The derived CLTs are a basis for further (asymptotic) statistical inference of the tessellation models and the related functionals. In particular, asymptotic confidence intervals and tests with respect to certain intensities (mean values per unit volume) are derived. Since the mentioned CLTs require certain conditions to hold and allow for statistical inference only within a certain tessellation model, a second part of this thesis sheds light on the problem of identifying an appropriate model for network data within a whole class of suitable models. In particular, a statistical fitting procedure for random tessellations is examined, which is based on simulation techniques and which can be verified via Monte Carlo tests.dc.description.abstract
Languageendc.language.iso
PublisherUniversität Ulmdc.publisher
LicenseStandard (Fassung vom 03.05.2003)dc.rights
Link to license texthttps://oparu.uni-ulm.de/xmlui/license_v1dc.rights.uri
KeywordNetwork modellingdc.subject
KeywordRandom tessellationdc.subject
Dewey Decimal GroupDDC 510 / Mathematicsdc.subject.ddc
LCSHCentral limit theoremdc.subject.lcsh
LCSHStochastic geometrydc.subject.lcsh
LCSHTessellations: Mathematicsdc.subject.lcsh
TitleAsymptotic analysis of stationary random tessellations with applications to network modellingdc.title
Resource typeDissertationdc.type
DOIhttp://dx.doi.org/10.18725/OPARU-388dc.identifier.doi
URNhttp://nbn-resolving.de/urn:nbn:de:bsz:289-vts-57022dc.identifier.urn
GNDStochastische Geometriedc.subject.gnd
GNDZufälliges Mosaikdc.subject.gnd
FacultyFakultät für Mathematik und Wirtschaftswissenschaftenuulm.affiliationGeneral
Date of activation2006-10-10T22:42:11Zuulm.freischaltungVTS
Peer reviewneinuulm.peerReview
Shelfmark print versionZ: J-H 11.271 ; W: W-H 9.385uulm.shelfmark
DCMI TypeTextuulm.typeDCMI
VTS ID5702uulm.vtsID
CategoryPublikationenuulm.category
Bibliographyuulmuulm.bibliographie


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