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On weak stationarity and weak isotropy of processes of convex bodies and cylinders

Part of: General convexity Stochastic processes Geometric probability and stochastic geometry

Published online by Cambridge University Press:  01 July 2016

Lars Michael Hoffmann
Lars Michael Hoffmann*
Affiliation:
Universität Karlsruhe (TH)
*
∗ Postal address: Institut für Algebra und Geometrie, Universität Karlsruhe (TH), 76128 Karlsruhe, Germany. Email address: lars.hoffmann@math.uni-karlsruhe.de
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Abstract

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Generalized local mean normal measures μz, z ∈ Rd, are introduced for a nonstationary process X of convex particles. For processes with strictly convex particles it is then shown that X is weakly stationary and weakly isotropic if and only if μz is rotation invariant for all z ∈ Rd. The paper is concluded by extending this result to processes of cylinders, generalizing Theorem 1 of Schneider (2003).

Keywords

Particle processcylinder processPoisson processmean normal measureweak stationarityweak isotropy

MSC classification

Primary: 60D05: Geometric probability and stochastic geometry
Secondary: 52A22: Random convex sets and integral geometry 60G55: Point processes
Type
Stochastic Geometry and Statistical Applications
Information
Advances in Applied Probability , Volume 39 , Issue 4 , December 2007 , pp. 864 - 882
Copyright
Copyright © Applied Probability Trust 2007 

References

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