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The mean number of maxima above high levels in Gaussian random fields

Published online by Cambridge University Press:  14 July 2016

A. M. Hasofer
A. M. Hasofer*
Affiliation:
University of New South Wales
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Abstract

An asymptotic formula for the mean number of maxima above a level of an n-dimensional stationary Gaussian field has been given by Nosko without proof. In this note a short general proof of this formula is given.

Keywords

RANDOM FIELDSMAXIMA ABOVE A LEVELGAUSSIAN PROCESSES
Type
Short Communications
Information
Journal of Applied Probability , Volume 13 , Issue 2 , June 1976 , pp. 377 - 379
Copyright
Copyright © Applied Probability Trust 1976 

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References

[1] Belyayev, Yu. K. (1972) Point processes and first passage problems. Proc. 6th Berkeley Symp. Math. Statist. Prob. 2, 1–17.Google Scholar
[2] Nosko, V. P. (1969) The characteristics of excursions of Gaussian homogeneous fields above a high level. Proceedings of the U.S.S.R.–Japan Symposium on Probability , Novosibirsk. Google Scholar
[3] Nosko, V. P. (1970) ‘Shines’ of Gaussian random fields. Vestnik Moskov. Univ. Ser. I Mat. Meh. 25, 4, 18–22.Google Scholar