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ArticleOriginal scientific text

Title

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

Authors 1, 2

Affiliations

  1. Department of Mathematics, Hampton University, Hampton, Virginia 23668, U.S.A.
  2. The Hugo Steinhaus Center for Stochastic Methods, Wrocław Technical University, Wrocław, Poland

Abstract

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 as a unitary deformation of a periodic function is derived and is related to the correspondence mentioned above. Some consequences of this representation are discussed.

Keywords

ENG
periodically correlated process, stationary process, imprimitivity theorem

Bibliography

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Studia Mathematica
1999/136/1
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Pages:
71-86
Main language of publication
English
Received
1998-10-26
Published
1999
Exact and natural sciences