Stochastic Mappings and Random Distribution Fields II: Stationarity

Abstract

This paper treats the stationarity and stationarily cross correlatedness of infinite variate stochastic mappings. Moreover, for the case of infinite variate random distribution fields, a particular form for the operator cross covariance distribution is given, from which a Kolmogorov type isomorphism theorem and spectral representations are derived. Finally, it is proved that the stationarity of an infinite variate random distribution field is passed onto the summands in the general Wold decomposition.