Intrinsic volumes of the maximal polytope process in higher dimensional STIT tessellations

Autor(en): Schreiber, Tomasz
Thaele, Christoph
Stichwörter: Central limit theory; Integral geometry; intrinsic volumes; Iteration/Nesting; Markov process; Martingale; Mathematics; Random tessellation; Statistics & Probability; Stochastic geometry; Stochastic stability
Erscheinungsdatum: 2011
Herausgeber: ELSEVIER SCIENCE BV
Journal: STOCHASTIC PROCESSES AND THEIR APPLICATIONS
Volumen: 121
Ausgabe: 5
Startseite: 989
Seitenende: 1012
Zusammenfassung: 
Stationary and isotropic iteration stable random tessellations are considered, which are constructed by a random process of iterative cell division. The collection of maximal polytopes at a fixed time t within a convex window W subset of R-d is regarded and formulas for mean values, variances and a characterization of certain covariance measures are proved. The focus is on the case d >= 3, which is different from the planar one, treated separately in Schreiber and Thale (2010) [12]. Moreover, a limit theorem for suitably resealed intrinsic volumes is established, leading - in sharp contrast to the situation in the plane to a non-Gaussian limit. (C) 2011 Elsevier B.V. All rights reserved.
ISSN: 03044149
DOI: 10.1016/j.spa.2011.01.001

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