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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
Abstract
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).
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- Stochastic Geometry and Statistical Applications
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- Copyright © Applied Probability Trust 2007
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