SECOND-ORDER THEORY FOR ITERATION STABLE TESSELLATIONS

DC FieldValueLanguage
dc.contributor.authorSchreiber, Tomasz
dc.contributor.authorThaele, Christoph
dc.date.accessioned2021-12-23T16:06:48Z-
dc.date.available2021-12-23T16:06:48Z-
dc.date.issued2012
dc.identifier.issn02084147
dc.identifier.urihttps://osnascholar.ub.uni-osnabrueck.de/handle/unios/7561-
dc.description.abstractThis paper deals with iteration stable (STIT) tessellations, and, more generally, with a certain class of tessellations that are infinitely divisible with respect to iteration. They form a new, rich and flexible family of space-time models considered in stochastic geometry. The previously developed martingale tools are used to study second-order properties of STIT tessellations. A general formula for the variance of the total surface area of cell boundaries inside an observation window is shown. This general expression is combined with tools from integral geometry to derive exact and asymptotic second-order formulas in the stationary and isotropic regime. Also a general formula for the pair-correlation function of the surface measure is found.
dc.language.isoen
dc.publisherWYDAWNICTWO UNIWERSYTETU WROCLAWSKIEGO
dc.relation.ispartofPROBABILITY AND MATHEMATICAL STATISTICS-POLAND
dc.subjectChord-power integral
dc.subjectCONSTRUCTION
dc.subjectintegral geometry
dc.subjectiteration/nesting
dc.subjectLIMIT
dc.subjectmartingale theory
dc.subjectMathematics
dc.subjectpair-correlation function
dc.subjectrandom geometry
dc.subjectrandom tessellation
dc.subjectStatistics & Probability
dc.subjectSTIT TESSELLATIONS
dc.subjectstochastic geometry
dc.subjectstochastic stability
dc.titleSECOND-ORDER THEORY FOR ITERATION STABLE TESSELLATIONS
dc.typejournal article
dc.identifier.isiISI:000321014000007
dc.description.volume32
dc.description.issue2
dc.description.startpage281
dc.description.endpage300
dc.contributor.researcheridD-7435-2014
dc.publisher.placePL. UNIWERSYTECKI 15, WROCLAW, 50-137, POLAND
dcterms.isPartOf.abbreviationProb. Math. Stat..
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