On generalising the notion of upcrossings to random fields

Author:

Adler Robert J.

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.

Publisher

Cambridge University Press (CUP)

Subject

Applied Mathematics,Statistics and Probability

Reference28 articles.

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2. Upcrossing probabilities for stationary Gaussian processes

3. On the possibility of using the Morse inequalities for the estimation of the number of excursions of a random field in a domain;Nosko;Theor. Prob. Appl.,1973

4. Nosko V. P. (1969) The characteristics of excursions of Gaussian homogeneous fields above a high level. Proceedings of the USSR–Japan Symposium on Probability, Novosibirsk.

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