Intrinsic volumes of the maximal polytope process in higher dimensional STIT tessellations
- Schreiber, Tomasz Nicolaus Copernicus University, Toruń, Poland
- Thäle, Christoph University of Fribourg, Switzerland
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19.01.2011
Published in:
- Stochastic Processes and their Applications. - 2011, vol. 121, no. 5, p. 989-1012
Central limit theory
Integral geometry
Intrinsic volumes
Iteration/Nesting
Markov process
Martingale
Random tessellation
Stochastic stability
Stochastic geometry
English
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 View the MathML source 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 Thäle (2010) [12]. Moreover, a limit theorem for suitably rescaled intrinsic volumes is established, leading — in sharp contrast to the situation in the plane — to a non-Gaussian limit.Keywords: Central limit theory; Integral geometry; Intrinsic volumes; Iteration/Nesting; Markov process; Martingale; Random tessellation; Stochastic stability; Stochastic geometry.
- Faculty
- Faculté des sciences et de médecine
- Department
- Département de Mathématiques
- Language
-
- English
- Classification
- Mathematics
- License
- License undefined
- Identifiers
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- RERO DOC 21810
- DOI 10.1016/j.spa.2011.01.001
- Persistent URL
- https://folia.unifr.ch/unifr/documents/301710
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