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Densities of mixed volumes for Boolean models

Published online by Cambridge University Press:  01 July 2016

Wolfgang Weil*
Affiliation:
Universität Karlsruhe
*
Postal address: Mathematisches Institut II, Universität Karlsruhe, D-76128 Karlsruhe, Germany. Email address: [email protected]

Abstract

In generalization of the well-known formulae for quermass densities of stationary and isotropic Boolean models, we prove corresponding results for densities of mixed volumes in the stationary situation and show how they can be used to determine the intensity of non-isotropic Boolean models Z in d-dimensional space for d = 2, 3, 4. We then consider non-stationary Boolean models and extend results of Fallert on quermass densities to densities of mixed volumes. In particular, we present explicit formulae for a planar inhomogeneous Boolean model with circular grains.

Type
Stochastic Geometry and Statistical Applications
Copyright
Copyright © Applied Probability Trust 2001 

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