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Stationary iterated tessellations

Part of: Geometric probability and stochastic geometry Operations research and management science Stochastic processes

Published online by Cambridge University Press:  22 February 2016

Roland Maier  and
Volker Schmidt
Roland Maier*
Affiliation:
University of Ulm
Volker Schmidt*
Affiliation:
University of Ulm
*
∗ Postal address: Department of Stochastics, University of Ulm, Helmholtzstr. 18, D-89069 Ulm, Germany.
∗ Postal address: Department of Stochastics, University of Ulm, Helmholtzstr. 18, D-89069 Ulm, Germany.
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Abstract

The iteration of random tessellations in ℝd is considered, where each cell of an initial tessellation is further subdivided into smaller cells by so-called component tessellations. Sufficient conditions for stationarity and isotropy of iterated tessellations are given. Formulae are derived for the intensities of their facet processes, and for the expected intrinsic volumes of their typical facets. Particular emphasis is put on two special cases: superposition and nesting of tessellations. Bernoulli thinning of iterated tessellations is also considered.

Keywords

Stochastic geometryrandom tessellationiterationstationarityisotropyfacet processintensity formulaquermassdensitytypical facetsuperpositionnestingBernoulli thinning

MSC classification

Primary: 60D05: Geometric probability and stochastic geometry
Secondary: 60G55: Point processes 90B15: Network models, stochastic

Information

Type
Stochastic Geometry and Statistical Applications
Information
Advances in Applied Probability , Volume 35 , Issue 2 , June 2003 , pp. 337 - 353
Copyright
Copyright © Applied Probability Trust 2003 

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