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On the envelope of a Gaussian random field

Published online by Cambridge University Press:  14 July 2016

R. J. Adler
R. J. Adler*
Affiliation:
CSIRO Division of Mathematics and Statistics, Lindfield
*
∗Now at the University of New South Wales.
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Abstract

For homogeneous, two-dimensional random field ξ(t), t ∈ R2 we develop the ‘half' spectral theory sufficient to rigorously define its envelope η (t). We then specialise to the case of ξ Gaussian, which implies η is Rayleigh, and consider the mean value of a certain characteristic of the sets {t:η(t) ≧ u} (u ≧ 0). From this we deduce some qualitative information about the sample path behaviour of the Rayleigh field η .

Keywords

RANDOM FIELDSENVELOPESGAUSSIAN PROCESSESSPECTRAL REPRESENTATIONEXCURSION SETSEXCURSION CHARACTERISTICSMEAN VALUESHIGH-LEVEL EXCURSIONS
Type
Research Papers
Information
Journal of Applied Probability , Volume 15 , Issue 3 , September 1978 , pp. 502 - 513
Copyright
Copyright © Applied Probability Trust 1978 

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