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

Tomasz Schreiber and Christoph Thäle

Stochastic Processes and their Applications, 2011, vol. 121, issue 5, 989-1012

Abstract: 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 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)Â [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 (search for similar items in EconPapers)
Date: 2011
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