Hostname: page-component-cd9895bd7-8ctnn Total loading time: 0 Render date: 2024-12-18T16:22:20.098Z Has data issue: false hasContentIssue false
  • English
  • Français

Joint distribution of successive zero crossing distances for stationary Gaussian processes

Published online by Cambridge University Press:  14 July 2016

Igor Rychlik
Igor Rychlik*
Affiliation:
University of Lund
*
∗Postal address: Dept. of Mathematical Statistics, University of Lund, Box 118, S-221 00 Lund, Sweden.
Get access Rights & Permissions [Opens in a new window]

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.

Keywords

CROSSINGSFATIGUEMAXIMAPERIODS ANALYSISREGRESSIONWAVELENGTH
Type
Research Papers
Information
Journal of Applied Probability , Volume 24 , Issue 2 , June 1987 , pp. 378 - 385
Copyright
Copyright © Applied Probability Trust 1987 

Access options

Get access to the full version of this content by using one of the access options below. (Log in options will check for institutional or personal access. Content may require purchase if you do not have access.)

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.Google Scholar
[2] Lindgren, G. (1972) Wave-length and amplitude in Gaussian noise. Adv. Appl. Prob. 4, 81–108.Google 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, 1–45.Google Scholar
[4] Lindgren, G. and Rychlik, I. (1982) Wave characteristic distributions for Gaussian waves — wave-length, amplitude, and steepness. Ocean Engng. 9, 411–432.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, 1–12.Google Scholar
[6] Rychlik, I. (1987) Regression approximations of wavelength and amplitude distributions. Adv. Appl. Prob. 19(2).CrossRefGoogle Scholar