Shape-driven nested Markov tessellations

Autor(en): Schreiber, Tomasz
Thaele, Christoph
Stichwörter: 60J75; CONSTRUCTION; ITERATION; Markov process; Mathematics; Mathematics, Applied; mean values; nested tessellation; Primary: 60D05; random tessellation; Secondary: 60J25; Statistics & Probability; stochastic geometry
Erscheinungsdatum: 2013
Herausgeber: TAYLOR & FRANCIS LTD
Journal: STOCHASTICS-AN INTERNATIONAL JOURNAL OF PROBABILITY AND STOCHASTIC PROCESSES
Volumen: 85
Ausgabe: 3
Startseite: 510
Seitenende: 531
Zusammenfassung: 
A 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.
ISSN: 17442508
DOI: 10.1080/17442508.2011.654344

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