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

Published online by Cambridge University Press:  01 July 2016

Lars Michael Hoffmann*
Affiliation:
Universität Karlsruhe (TH)
*
Postal address: Institut für Algebra und Geometrie, Universität Karlsruhe (TH), 76128 Karlsruhe, Germany. Email address: [email protected]
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Abstract

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Generalized local mean normal measures μz, zRd, 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 zRd. The paper is concluded by extending this result to processes of cylinders, generalizing Theorem 1 of Schneider (2003).

Type
Stochastic Geometry and Statistical Applications
Copyright
Copyright © Applied Probability Trust 2007 

References

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