SECOND-ORDER THEORY FOR ITERATION STABLE TESSELLATIONS

Autor(en): Schreiber, Tomasz
Thaele, Christoph
Stichwörter: Chord-power integral; CONSTRUCTION; integral geometry; iteration/nesting; LIMIT; martingale theory; Mathematics; pair-correlation function; random geometry; random tessellation; Statistics & Probability; STIT TESSELLATIONS; stochastic geometry; stochastic stability
Erscheinungsdatum: 2012
Herausgeber: WYDAWNICTWO UNIWERSYTETU WROCLAWSKIEGO
Journal: PROBABILITY AND MATHEMATICAL STATISTICS-POLAND
Volumen: 32
Ausgabe: 2
Startseite: 281
Seitenende: 300
Zusammenfassung: 
This 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.
ISSN: 02084147

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