Tail processes and tail measures: An approach via Palm calculus

Abstract Using an intrinsic approach, we study some properties of random fields which appear as tail regularly varying stationary fields. The index set is allowed to be a general locally compact Hausdorff Abelian group $${\mathbb G}$$ G . values are taken in measurable cone, equipped with pseudo norm. We first discuss Palm formulas for the exceedance measure $$\xi$$ ξ associated (measurable) field $$Y=(Y_s)_{s\in {\mathbb G}}$$ Y = ( s ) ∈ It important allow underlying $$\sigma$$ σ -finite. Then proceed (defined on probability space) spectrally decomposable, sense motivated by extreme value theory. characterize mass-stationarity terms suitable version classical Mecke equation. also show that homogeneous, measure. then establishing and studying spectral representation measures characterizing moving shift representation. Finally anchoring maps candidate extremal index.