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Slepian models for X2-processes with dependent components with application to envelope upcrossings

Published online by Cambridge University Press:  14 July 2016

Georg Lindgren
Georg Lindgren*
Affiliation:
University of Lund
*
∗Postal address: Department of Mathematical Statistics, University of Lund, Box 118, S-221 00 Lund, Sweden.
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Abstract

A Slepian model for the local behaviour near the level upcrossings of a x2-process with dependent Gaussian components is presented. In case of independent components, this model is shown to take on a rather simple form, thereby simplifying earlier results by Aronowich and Adler.

The Slepian model is applied to the envelope of a stationary Gaussian process and used to approximate the probability of ‘empty' envelope upcrossings, i.e. the probability that an envelope upcrossing is not followed by a level crossing in the original process.

Keywords

LEVEL CROSSINGRELIABILITY
Type
Research Papers
Information
Journal of Applied Probability , Volume 26 , Issue 1 , March 1989 , pp. 36 - 49
Copyright
Copyright © Applied Probability Trust 1989 

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Footnotes

Part of this work was carried out during a visit to the Department of Structural Engineering, the Technical University of Denmark, Lyngby.

References

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