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

Abstract

Generalized local mean normal measures μ z , z ∈ R d , 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 μ z is rotation invariant for all z ∈ R d . The paper is concluded by extending this result to processes of cylinders, generalizing Theorem 1 of Schneider (2003).