A Note on Metric Transitivity for Stationary Gaussian Processes on Groups

Abstract

Maruyama (1949) and Grenander (1950) derive necessary and sufficient conditions for stationary Gaussian processes on the real line or the integers to be metrically transitive. Their work is based on ergodic theorems for such processes. This paper studies conditions for metric transitivity for stationary Gaussian proceses for which there are no ergodic theorems. Instead the work is based on results on the absolute continuity of measures corresponding to random processes.