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A uniqueness problem for the envelope of an oscillatory process

Published online by Cambridge University Press:  14 July 2016

A. M. Hasofer
A. M. Hasofer*
Affiliation:
The University of New South Wales
*
∗ Postal address: School of Mathematics, Department of Statistics, The University of New South Wales, P.O.Box 1, Kensington, N.S.W. 2033, Australia.
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Abstract

In a previous paper, the author has described a method for obtaining envelope processes for oscillatory stochastic processes. These are processes which can be represented as the output of a time-varying linear filter whose input is a stationary process.

It is shown in this paper that the proposed definition of the envelope process may not be unique, but may depend on the particular representation of the oscillatory process chosen.

It is then shown that for a class of oscillatory processes which is of particular interest, the class of transient processes, there is a class of natural representations which all lead to a unique envelope process.

Keywords

NON-STATIONARY STOCHASTIC PROCESSESTIME-VARYING FILTERSENVELOPE PROCESSES

Information

Type
Research Papers
Information
Journal of Applied Probability , Volume 16 , Issue 4 , December 1979 , pp. 822 - 829
Copyright
Copyright © Applied Probability Trust 1979 

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References

[1] Arens, R. (1957) Complex processes for envelopes of normal noise. IRE Trans. Inf. Theory 3, 204–207.Google Scholar
[2] Cramer, H. and Leadbetter, M. R. (1967) Stationary and Related Stochastic Processes. Wiley, New York.Google Scholar
[3] Hasofer, A. M. and Petocz, P. (1978) The envelope of an oscillatory process and its upcrossings (abstract). Adv. Appl. Prob. 10, 711–716.CrossRefGoogle Scholar
[4] Priestley, M. B. (1965) Evolutionary spectra and non-stationary processes. J. R. Statist. Soc. B 27, 204–229.Google Scholar
[5] Yang, J. N. (1972) Non-stationary envelope process and first-excursion probability. J. Structural Mech. 1, 231–248.Google Scholar