Mutual subordination of multivariate stationary processes over any locally compact abelian group

Abstract

Our purpose is to extend Kolmogorov's theorem [5, Th. 10] on mutual subordination for univariate weakly stationary stochastic processes over the (discrete) group of integers to multivariate processes over any (Hausdorff) locally compact abelian (lca) group. This extension is given in Theorems (1.12) and (3.4) below. We shall lean heavily on the joint paper [10] on the decomposition of matricial measures, to which the present paper may be regarded as a sequel.