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November 2013 Geometry of iteration stable tessellations: Connection with Poisson hyperplanes
Tomasz Schreiber, Christoph Thäle
Bernoulli 19(5A): 1637-1654 (November 2013). DOI: 10.3150/12-BEJ424

Abstract

Since the seminal work by Nagel and Weiss, the iteration stable (STIT) tessellations have attracted considerable interest in stochastic geometry as a natural and flexible, yet analytically tractable model for hierarchical spatial cell-splitting and crack-formation processes. We provide in this paper a fundamental link between typical characteristics of STIT tessellations and those of suitable mixtures of Poisson hyperplane tessellations using martingale techniques and general theory of piecewise deterministic Markov processes (PDMPs). As applications, new mean values and new distributional results for the STIT model are obtained.

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Tomasz Schreiber. Christoph Thäle. "Geometry of iteration stable tessellations: Connection with Poisson hyperplanes." Bernoulli 19 (5A) 1637 - 1654, November 2013. https://doi.org/10.3150/12-BEJ424

Information

Published: November 2013
First available in Project Euclid: 5 November 2013

zbMATH: 1291.60021
MathSciNet: MR3129028
Digital Object Identifier: 10.3150/12-BEJ424

Rights: Copyright © 2013 Bernoulli Society for Mathematical Statistics and Probability

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Vol.19 • No. 5A • November 2013
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