Ergodic theorems for spatial processes

Abstract

We investigate the ergodic properties of spatial processes, i.e. stochastic processes with an index set of bounded Borel subsets in ℝv, and prove mean and individual ergodic theorems for them. As important consequences we get a generalization of McMillan's theorem due to Fritz [4]; the existence of specific energy for a large class of interactions in the case of marked point processes in ℝv and the existence of the specific Minkowski Quermaßintegrals for Boolean models in ℝv with convex, compact grains. © 1979 Springer-Verlag.