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Non-Stationary Processes and Spectrum

Published online by Cambridge University Press:  20 November 2018

K. Nagabhushanam  and
C. S. K. Bhagavan
K. Nagabhushanam
Affiliation:
Andhra University, Waltair, India
C. S. K. Bhagavan
Affiliation:
Andhra University, Waltair, India
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In 1964, L. J. Herbst (3) introduced the generalized spectral density Function

1

for a non-stationary process {X(t)} denned by

1

where {η(t)} is a real Gaussian stationary process of discrete parameter and independent variates, the (a;)'s and (σj)'s being constants, the latter, which are ordered in time, having their moduli less than a positive number M.

Type
Research Article
Information
Canadian Journal of Mathematics , Volume 20 , 1968 , pp. 1203 - 1206
Copyright
Copyright © Canadian Mathematical Society 1968

References

1. Gnedenko, B. V., The theory of probability (Chelsea, New York, 1962).Google Scholar
2. Grenander, U. and Rosenblatt, M., Statistical analysis of stationary time series (Wiley, New York, 1957).10.1063/1.3060405CrossRefGoogle Scholar
3. Herbst, L. J., Spectral analysis in the presence of variance fluctuations, J. Roy. Statist. Soc. Ser. B 21 (1964), 354–360.Google Scholar
4. Priestley, M. B., Evolutionary spectra and non-stationary processes, J. Roy. Statist. Soc. Ser. B 27 (1965), 204–237.Google Scholar