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Covariance function and ergodicity of asymptotically stationary random fields

Published online by Cambridge University Press:  17 April 2009

V.V. Anh  and
K.E. Lunney
V.V. Anh
Affiliation:
School of Mathematics, Queensland University of Technology, GPO Box 2434 Brisbane Qld 4001, Australia
K.E. Lunney
Affiliation:
School of Mathematics, Queensland University of Technology, GPO Box 2434 Brisbane Qld 4001, Australia
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Abstract

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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.

Type
Research Article
Information
Bulletin of the Australian Mathematical Society , Volume 44 , Issue 1 , August 1991 , pp. 49 - 62
Copyright
Copyright © Australian Mathematical Society 1991

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