SPECTRAL REPRESENTATION AND ERGODICITY OF ASYMPTOTICALLY STATIONARY PROCESSES

A second order process with mean zero and covariance is asymptotically stationary if lim ds exists for every; this limit then defines the covariance function of the process. The paper establishes the spectral representation for the covariance function and a mean ergodic theorem for the process. When stationarity is assumed, the results reduce to the well-known corresponding theorems for stationary processes.