Displaying similar documents to “A remark concerning uniqueness of the Wold decomposition of finite-dimensional stationary processes.”

On measure-preserving transformations and doubly stationary symmetric stable processes

A. Gross, A. Weron (1995)

Studia Mathematica

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In a 1987 paper, Cambanis, Hardin and Weron defined doubly stationary stable processes as those stable processes which have a spectral representation which is itself stationary, and they gave an example of a stationary symmetric stable process which they claimed was not doubly stationary. Here we show that their process actually had a moving average representation, and hence was doubly stationary. We also characterize doubly stationary processes in terms of measure-preserving regular...

On spectral bandwidth of a stationary random process

Vladimír Klega (1983)

Aplikace matematiky

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The irregularity coefficient is one of the numerical characteristics of the spectral bandwith of a stationary random process. Its basic properties are investigated and the application to the dichotomic classification of a process into narrow-band and wide-band ones is given. Further, its behaviour is analyzed for sufficiently wide classes of stationary processes whose spectral densities frequently appear both in theory and applications.

Induced stationary process and structure of locally square integrable periodically correlated processes

Andrzej Makagon (1999)

Studia Mathematica

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A one-to-one correspondence between locally square integrable periodically correlated (PC) processes and a certain class of infinite-dimensional stationary processes is obtained. The correspondence complements and clarifies Gladyshev's known result [3] describing the correlation function of a continuous periodically correlated process. In contrast to Gladyshev's paper, the procedure for explicit reconstruction of one process from the other is provided. A representation of a PC process...