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On generalising the notion of upcrossings to random fields

Published online by Cambridge University Press:  01 July 2016

Robert J. Adler
Robert J. Adler*
Affiliation:
University of New South Wales
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Abstract

The aim of the current paper is twofold. Primarily we wish to extend some of our earlier results on excursions of random fields and introduce a more powerful technique for obtaining the mean value of a certain characteristic of these excursions. Since these results can also be used to tie together the scattered results of previous authors we also include a full review of earlier work in this field.

Keywords

RANDOM FIELDSLEVEL CROSSINGSEXCURSION SETSEXCURSION CHARACTERISTICGAUSSIAN FIELDSMEAN VALUESHIGH LEVEL EXCURSIONS
Type
Research Article
Information
Advances in Applied Probability , Volume 8 , Issue 4 , December 1976 , pp. 789 - 805
Copyright
Copyright © Applied Probability Trust 1976 

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