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Slepian models for non-stationary Gaussian processes

Part of: Stochastic processes

Published online by Cambridge University Press:  14 July 2016

Tamar Gadrich  and
Robert J. Adler
Tamar Gadrich*
Affiliation:
Technion–Israel Institute of Technology
Robert J. Adler*
Affiliation:
Technion–Israel Institute of Technology
*
∗ Postal address: Faculty of Industrial Engineering and Management, Technion–Israel Institute of Technology, Haifa 32000, Israel.
∗ Postal address: Faculty of Industrial Engineering and Management, Technion–Israel Institute of Technology, Haifa 32000, Israel.
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Abstract

We give explicit expressions for the Slepian model process of non-stationary Gaussian processes following level crossings and local maxima. We also include a detailed analysis of the high-level case.

Keywords

UPCROSSINGLOCAL MAXIMUM

MSC classification

Secondary: 60G10: Stationary processes 60G17: Sample path properties
Type
Research Papers
Information
Journal of Applied Probability , Volume 30 , Issue 1 , March 1993 , pp. 98 - 111
Copyright
Copyright © Applied Probability Trust 1993 

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Footnotes

Research supported in part by US-Israel Binational Science Foundation (89–00298) and U.S. Air Force Office of Scientific Research (89–0261).

References

[1] Abramowitz, M. and Stegun, I. A. (1965) Handbook of Mathematical Functions. Dover, New York.Google Scholar
[2] Cramér, H. and Leadbetter, M. R. (1967) Stationary and Related Stochastic Processes. Wiley, New York.Google Scholar
[3] Grigoriu, M. (1989) Reliability of Daniels systems subject to quasistatic and dynamic non-stationary Gaussian load processes. Prob. Eng. Mech. 4, 128–134.CrossRefGoogle Scholar
[4] Kac, M. and Slepian, D. (1959) Large excursions of Gaussian processes. Ann. Math. Statist. 30, 1215–1228.CrossRefGoogle Scholar
[5] Leadbetter, M. R., Lindgren, G. and Rootzen, H. (1983) Extremes and Related Properties of Random Sequences and Processes. Springer-Verlag, Berlin.Google Scholar
[6] Lindgren, G. (1970) Some properties of a normal process near a local maximum. Ann. Math. Statist. 41, 1870–1883.Google Scholar
[7] Lindgren, G. (1979) Prediction of level crossings for normal processes containing deterministic components. Adv. Appl. Prob. 11, 93–117.Google Scholar
[8] Rao, C. R. (1965) Linear Statistical Inference and Its Applications. Wiley, New York.Google Scholar
[9] Slepian, D. (1962) On the zeros of Gaussian noise. In Time Series Analysis, ed. Rosenblatt, M., pp. 104–115, Wiley, New York.Google Scholar