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Nonstationary Poisson hyperplanes and their induced tessellations

Part of: Geometric probability and stochastic geometry

Published online by Cambridge University Press:  01 July 2016

Rolf Schneider
Rolf Schneider*
Affiliation:
Albert-Ludwigs-Universität Freiburg
*
∗ Postal address: Mathematisches Institut, Albert-Ludwigs-Universität, Eckerstr. 1, D-79104 Freiburg, Germany. Email address: [email protected]
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Abstract

Results about stationary Poisson hyperplane processes and the induced hyperplane mosaics are extended to the case where, instead of stationarity, it is only assumed that the intensity measure has a (possibly continuous) density with respect to some translation-invariant measure. Intensities and quermass densities, which are constant in the stationary case, are then replaced by functions. In a similar way, the associated zonoid (Matheron's Steiner convex set) is generalized.

Keywords

Hyperplane processPoisson processintensityintersection processhyperplane mosaicface processquermass densityassociated zonoidSteiner convex set

MSC classification

Primary: 60D05: Geometric probability and stochastic geometry
Type
Stochastic Geometry and Statistical Applications
Information
Advances in Applied Probability , Volume 35 , Issue 1 , March 2003 , pp. 139 - 158
Copyright
Copyright © Applied Probability Trust 2003 

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