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Joint distribution of successive zero crossing distances for stationary Gaussian processes

Published online by Cambridge University Press:  14 July 2016

Igor Rychlik*
Affiliation:
University of Lund
*
Postal address: Dept. of Mathematical Statistics, University of Lund, Box 118, S-221 00 Lund, Sweden.

Abstract

As has been shown by de Maré, in a stationary Gaussian process the length of the successive zero-crossing intervals cannot be independent, except for the degenerate case of a pure cosine process. However, no closed-form expression of the distribution of these quantities is known at present. In this paper we present an accurate explicit approximative formula, derived by replacing the Slepian model process by its regression curve.

Type
Research Papers
Copyright
Copyright © Applied Probability Trust 1987 

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Footnotes

Research supported in part by the National Swedish Board for Technical Development under contract No 83-3042.

References

[1] Leadbetter, M. R., Lindgren, G. and Rootzen, H. (1983) Extremes and Related Properties of Random Sequences and Processes. Springer-Verlag, New York.CrossRefGoogle Scholar
[2] Lindgren, G. (1972) Wave-length and amplitude in Gaussian noise. Adv. Appl. Prob. 4, 81108.CrossRefGoogle Scholar
[3] Lindgren, G. and Holmström, K. (1978) WAMP — a computer program for wavelength and amplitude analysis of Gaussian waves. Univ. Ume? Stat. Res. Rep. 1978–9, 145.Google Scholar
[4] Lindgren, G. and Rychlik, I. (1982) Wave characteristic distributions for Gaussian waves — wave-length, amplitude, and steepness. Ocean Engng. 9, 411432.CrossRefGoogle Scholar
[5] Maré, J. De (1974) When are the successive zero-crossings intervals of a Gaussian process independent? Univ. Lund Stat. Res. Rep. 1974:3, 112.Google Scholar
[6] Rychlik, I. (1987) Regression approximations of wavelength and amplitude distributions. Adv. Appl. Prob. 19(2).CrossRefGoogle Scholar
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