Construction and Characterisation of Stationary and Mass-Stationary Random Measures on ${\mathbb R}^d$

Abstract

Mass-stationarity means that the origin is at a typical location in the mass of a random measure. It is an intrinsic characterisation of Palm versions with respect to stationary random measures. Stationarity is the special case when the random measure is Lebesgue measure. The paper presents constructions of stationary and mass-stationary versions through change of measure and change of origin. Further, the paper considers characterisations of mass-stationarity by distributional invariance under preserving shifts agains stationary independent backgrounds.