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The iteration of random tessellations and a construction of a homogeneous process of cell divisions

Part of: Stochastic processes Geometric probability and stochastic geometry

Published online by Cambridge University Press:  01 July 2016

Joseph Mecke ,
Werner Nagel  and
Viola Weiss
Joseph Mecke*
Affiliation:
Friedrich-Schiller-Universität Jena
Werner Nagel*
Affiliation:
Friedrich-Schiller-Universität Jena
Viola Weiss*
Affiliation:
Fachhochschule Jena
*
∗ Postal address: Fakultät für Mathematik und Informatik, Friedrich-Schiller-Universität Jena, D-07737 Jena, Germany.
∗ Postal address: Fakultät für Mathematik und Informatik, Friedrich-Schiller-Universität Jena, D-07737 Jena, Germany.
∗∗∗ Postal address: Fachhochschule Jena, D-07703 Jena, Germany.
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Abstract

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A random tessellation of ℝd is said to be homogeneous if its distribution is invariant under all shifts of ℝd. The iteration of homogeneous random tessellations is described in a new manner that makes it evident that the resulting random tessellation is homogeneous again. Furthermore, a tessellation-valued process is constructed, the random states of which are homogeneous random tessellations stable under iteration (STIT). It can be interpreted as a process of subsequent division of cells.

Keywords

Stochastic geometryrandom tessellationtessellation-valued stochastic processPoisson point processiteration of tessellationsnesting of tessellationsstability of distributions

MSC classification

Primary: 60D05: Geometric probability and stochastic geometry
Secondary: 60G55: Point processes
Type
Stochastic Geometry and Statistical Applications
Information
Advances in Applied Probability , Volume 40 , Issue 1 , March 2008 , pp. 49 - 59
Copyright
Copyright © Applied Probability Trust 2008 

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