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Covariance function and ergodicity of asymptotically stationary random fields
Published online by Cambridge University Press: 17 April 2009
Abstract
A class of second-order asymptotically stationary random fields is shown to contain the class of almost harmonisable random fields. A continuity theorem which leads to the spectral representation for the covariance function of asymptotically stationary random fields is established. A mean ergodic theorem for the fields is also given. When stationarity is assumed, the results reduce to the well-known corresponding theorems for stationary random fields.
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- Copyright © Australian Mathematical Society 1991
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