LIMIT THEOREMS FOR ITERATION STABLE TESSELLATIONS

Autor(en): Schreiber, Tomasz
Thaele, Christoph
Stichwörter: 2ND-ORDER PROPERTIES; CELLS; Central limit theorem; CONSTRUCTION; functional limit theorem; iteration/nesting; Markov process; martingale theory; Mathematics; random tessellation; STATIONARY; Statistics & Probability; stochastic geometry; stochastic stability
Erscheinungsdatum: 2013
Herausgeber: INST MATHEMATICAL STATISTICS
Journal: ANNALS OF PROBABILITY
Volumen: 41
Ausgabe: 3B
Startseite: 2261
Seitenende: 2278
Zusammenfassung: 
The intent of this paper is to describe the large scale asymptotic geometry of iteration stable (STIT) tessellations in R-d, which form a rather new, rich and flexible class of random tessellations considered in stochastic geometry. For this purpose, martingale tools are combined with second-order formulas proved earlier to establish limit theorems for STIT tessellations. More precisely, a Gaussian functional central limit theorem for the surface increment process induced a by STIT tessellation relative to an initial time moment is shown. As second main result, a central limit theorem for the total edge length/facet surface is obtained, with a normal limit distribution in the planar case and, most interestingly, with a nonnormal limit showing up in all higher space dimensions.
ISSN: 00911798
DOI: 10.1214/11-AOP718

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