A simple condition for asymptotic optimality of linear predictions of random fields

Consider linear predictions of a stationary random field at an unobserved location in a bounded region as the observations become increasingly dense in that region. Suppose the ratio of the actual spectral density of the process to the spectral density used to generate the linear predictions tends to a positive finite constant as the frequency increases. Then the sequence of predictions based on the incorrect spectral density and the first n observations are asymptotically optimal as n --> [infinity].