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The structure of Gaussian fields near a level crossing

Published online by Cambridge University Press:  01 July 2016

Richard J. Wilson  and
Robert J. Adler
Richard J. Wilson*
Affiliation:
University of New South Wales
Robert J. Adler*
Affiliation:
Technion-Israel Institute of Technology
*
∗Postal address: Department of Statistics, School of Mathematics, University of New South Wales, P.O. Box 1, Kensington, NSW 2033, Australia.
∗∗Postal address: Faculty of Industrial Engineering and Management, Technion-Israel Institute of Technology, Haifa 32000, Israel.
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Abstract

In this paper, we investigate the behaviour of a Gaussian random field after an ‘upcrossing' of a particular level. In Section 1, we briefly discuss model processes and their background, and give a definition of an upcrossing of a level for random fields. A model field is constructed for the random field after an upcrossing of a level by using horizontal window conditioning in Section 2. The final section contains asymptotic distributions for the model field and for the location and height of the ‘closest' maximum to the upcrossing as the level becomes arbitrarily high.

Keywords

HOMOGENEOUSGAUSSIAN RANDOM FIELDUPCROSSINGHORIZONTAL WINDOW CONDITIONINGMODEL FIELD
Type
Research Article
Information
Advances in Applied Probability , Volume 14 , Issue 3 , September 1982 , pp. 543 - 565
Copyright
Copyright © Applied Probability Trust 1982 

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