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Level crossings of a constructed process

Published online by Cambridge University Press:  14 July 2016

Ken Sharpe
Ken Sharpe*
Affiliation:
University of Melbourne
*
∗Postal address: Department of Statistics, University of Melbourne, Parkville, Victoria 3052, Australia.
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Abstract

A method is presented for constructing a continuous, stationary process with a given rate of upcrossings at all levels and for which it is possible to find the exact distribution of the number of upcrossings, in an interval, at all levels.

Keywords

DISTRIBUTION OF UPCROSSINGSRATE OF UPCROSSINGS
Type
Short Communications
Information
Journal of Applied Probability , Volume 16 , Issue 1 , March 1979 , pp. 206 - 212
Copyright
Copyright © Applied Probability Trust 1979 

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Footnotes

This work was carried out while the author was a visitor in the Statistical Laboratory, University of Manchester.

References

Belyaev, Yu. K. (1963) Limit theorems for dissipative flows. Theory Prob. Appl. 8, 165–173.Google Scholar
Berman, S. M. (1974) Asymptotic independence of the numbers of high and low level crossings of stationary Gaussian processes. Ann. Math. Statist. 42, 927–945.Google Scholar
Cramér, H. and Leadbetter, M. R. (1967) Stationary and Related Stochastic Processes. Wiley, New York.Google Scholar
Hasofer, A. M. and Sharpe, K. (1969) The analysis of wind gusts. Austral. Meteorol. Mag. 17, 198–214.Google Scholar
Lindgren, G. (1972) Wave-length and amplitude in Gaussian noise. Adv. Appl. Prob. 4, 81–108.Google Scholar
Lindgren, G. (1974) Spectral moment estimation by means of level crossings. Biometrika 61, 401–418.CrossRefGoogle Scholar
Marcus, M. B. (1977) Level crossings of a stochastic process with absolutely continuous sample paths. Ann. Prob. 5, 52–71.Google Scholar
Sharpe, K. (1978) Some properties of the crossings process generated by a stationary ?2 process. Adv. Appl. Prob. 10, 373–391.Google Scholar
Volkonskii, V. A. and Rozanov, Yu. A. (1959), (1961) Some limit theorems for random functions. Theory Prob. Appl. 4, 178–197; 6, 186–198.CrossRefGoogle Scholar