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Generalised spectral analysis of fractional random fields

Part of: Inference from stochastic processes Stochastic processes

Published online by Cambridge University Press:  09 April 2009

V. V. Anh  and
K. E. Lunney
V. V. Anh
Affiliation:
School of Mathematics Queensland University of TechnologyGPO Box 2434 Brisbane, QLD 4001, Australia
K. E. Lunney
Affiliation:
School of Australian Environmental Studies Griffith UniversityNathan Brisbane, QLD 4111, Australia
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Abstract

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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.

MSC classification

Secondary: 60G60: Random fields 62M15: Spectral analysis
Type
Research Article
Information
Journal of the Australian Mathematical Society , Volume 62 , Issue 1 , February 1997 , pp. 64 - 83
Copyright
Copyright © Australian Mathematical Society 1997

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