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On the envelope of a Gaussian random field

Published online by Cambridge University Press:  14 July 2016

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

Abstract

For homogeneous, two-dimensional random field ξ(t), tR2 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 .

Type
Research Papers
Copyright
Copyright © Applied Probability Trust 1978 

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