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Generalised spectral analysis of fractional random fields
Published online by Cambridge University Press: 09 April 2009
Abstract
This paper considers a large class of non-stationary random fields which have fractal characteristics and may exhibit long-range dependence. Its motivation comes from a Lipschitz-Holder-type condition in the spectral domain.
The paper develops a spectral theory for the random fields, including a spectral decomposition, a covariance representation and a fractal index. From the covariance representation, the covariance function and spectral density of these fields are defined. These concepts are useful in multiscaling analysis of random fields with long-range dependence.
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- Research Article
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- Copyright © Australian Mathematical Society 1997