On the Strong Information Singularity of Certain Stationary Processes

In an exploratory paper, T. Berger studied discrete random processes which generate information slower than linearly with time. One of his objectives was to provide a physically meaningful definition of a deterministic process, and to this end he introduced the notion of strong information singularity. His work is supplemented by demonstrating that a large class of convariance stationary processes are strongly information singular with respect to a class of stationary Gaussian processes. One important consequence is that for a large class of covariance stationary processes the information rate equals that of the process associated with the Brownian motion component of the spectral representation.