Shape-driven nested Markov tessellations

DC FieldValueLanguage
dc.contributor.authorSchreiber, Tomasz
dc.contributor.authorThaele, Christoph
dc.date.accessioned2021-12-23T16:06:57Z-
dc.date.available2021-12-23T16:06:57Z-
dc.date.issued2013
dc.identifier.issn17442508
dc.identifier.urihttps://osnascholar.ub.uni-osnabrueck.de/handle/unios/7635-
dc.description.abstractA new and rather broad class of stationary random tessellations of the d-dimensional Euclidean space is introduced, which we call shape-driven nested Markov tessellations. Locally, these tessellations are constructed by means of a spatio-temporal random recursive split dynamics governed by a family of Markovian split kernel, generalizing thereby the - by now classical - construction of iteration stable random tessellations. By providing an explicit global construction of the tessellations, it is shown that under suitable assumptions on the split kernels (shape-driven), there exists a unique time-consistent whole-space tessellation-valued Markov process of stationary random tessellations compatible with the given split kernels. Beside the existence and uniqueness result, the typical cell and some aspects of the first-order geometry of these tessellations are in the focus of our discussion.
dc.language.isoen
dc.publisherTAYLOR & FRANCIS LTD
dc.relation.ispartofSTOCHASTICS-AN INTERNATIONAL JOURNAL OF PROBABILITY AND STOCHASTIC PROCESSES
dc.subject60J75
dc.subjectCONSTRUCTION
dc.subjectITERATION
dc.subjectMarkov process
dc.subjectMathematics
dc.subjectMathematics, Applied
dc.subjectmean values
dc.subjectnested tessellation
dc.subjectPrimary: 60D05
dc.subjectrandom tessellation
dc.subjectSecondary: 60J25
dc.subjectStatistics & Probability
dc.subjectstochastic geometry
dc.titleShape-driven nested Markov tessellations
dc.typejournal article
dc.identifier.doi10.1080/17442508.2011.654344
dc.identifier.isiISI:000320199800008
dc.description.volume85
dc.description.issue3
dc.description.startpage510
dc.description.endpage531
dc.contributor.researcheridD-7435-2014
dc.identifier.eissn17442516
dc.publisher.place2-4 PARK SQUARE, MILTON PARK, ABINGDON OR14 4RN, OXON, ENGLAND
dcterms.isPartOf.abbreviationStochastics
dcterms.oaStatusGreen Submitted
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