Geometry of iteration stable tessellations: Connection with Poisson hyperplanes

Autor(en): Schreiber, Tomasz
Thaele, Christoph
Stichwörter: CONSTRUCTION; infinite divisibility; iteration/nesting; Markov process; martingale theory; Mathematics; piecewise deterministic Markov process; random tessellation; Statistics & Probability; stochastic geometry; stochastic stability
Erscheinungsdatum: 2013
Herausgeber: INT STATISTICAL INST
Journal: BERNOULLI
Volumen: 19
Ausgabe: 5A
Startseite: 1637
Seitenende: 1654
Zusammenfassung: 
Since the seminal work by Nagel and Weiss, the iteration stable (STIT) tessellations have attracted considerable interest in stochastic geometry as a natural and flexible, yet analytically tractable model for hierarchical spatial cell-splitting and crack-formation processes. We provide in this paper a fundamental link between typical characteristics of STIT tessellations and those of suitable mixtures of Poisson hyperplane tessellations using martingale techniques and general theory of piecewise deterministic Markov processes (PDMPs). As applications, new mean values and new distributional results for the STIT model are obtained.
ISSN: 13507265
DOI: 10.3150/12-BEJ424

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