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Local maxima of stationary processes

Published online by Cambridge University Press:  24 October 2008

M. R. Leadbetter
M. R. Leadbetter
Affiliation:
Research Triangle Institute, Durham, N. Carolina, U.S.A.
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Abstract

Two natural definitions for the distribution function of the height of an ‘arbitrary local maximum’ of a stationary process are given and shown to be equivalent. It is further shown that the distribution function so defined has the correct frequency interpretation, for an ergodic process. Explicit results are obtained in the normal case.

Type
Research Article
Information
Mathematical Proceedings of the Cambridge Philosophical Society , Volume 62 , Issue 2 , April 1966 , pp. 263 - 268
Copyright
Copyright © Cambridge Philosophical Society 1966

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References

REFERENCES

(1)Doob, J. L.Stochastic processes (John Wiley and Sons, 1953).Google Scholar
(2)Kac, M. and Slepian, D.Large excursions of Gaussian processes. Ann. Math. Statist. 30 (1959), 1215–1228.CrossRefGoogle Scholar
(3)Khintchine, A. Y.Mathematical methods in the theory of mass servicing (1955). Translation Mathematical methods in the theory of queueing (1960). Griffin's Statistical Monograph No. 7.Google Scholar
(4)Leadbetter, M. R.On crossings of levels and curves by a wide class of stochastic processes. Research Triangle Institute Technical Report SU-181 No. 4 (1965). Also to appear in Ann. Math. Statist.Google Scholar
(5)Rice, S. O.Mathematical analysis of random noise. Bell System Tech. J. 24 (1945) 46–156.CrossRefGoogle Scholar
(6)Volkonski, V. A.An ergodic theorem on the distribution of the duration of fades. Teor. Veroyatnost i. Primenen. 5 (1960), 357–360.Google Scholar
(7)Ylvisaker, N. D.The expected number of zeros of a stationary Gaussian process. Ann. Math. Statist. 36 (1965), 1043–1046.CrossRefGoogle Scholar