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Linear transformations of locally stationary processes. (English) Zbl 0672.60043

A second order random process x(t) with zero mean is called a locally stationary process if its covariance function has the form \[ R_ x(t,s)=R_ x^{(1)}((s+t)/2)R_ x^{(2)}(s-t) \] where \(R_ x^{(1)}\geq 0\) and \(R_ x^{(2)}\) is some stationary covariance. Necessary and sufficient conditions are obtained under which a linear transformation of a harmonizable locally stationary process will also be a locally stationary one.
Reviewer: Ju.M.Ryẑov

MSC:

60G12 General second-order stochastic processes
60G10 Stationary stochastic processes
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References:

[1] R. A. Silverman: Locally stationary random processes. IRE Transactions of Information Theory IT-3 (1957), 3, 182-187.
[2] M. Loève: Probability Theory. D. van Nostrand, Toronto - New York- London, 1955. · Zbl 0066.10903
[3] J. Michálek: Spectral decomposition of locally stationary random processes. Kybernetika 22 (1986), 3, 244-255. · Zbl 0601.60036
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