Geodesic
Induced stationary process and structure of locally square integrable periodically correlated processes
Studia Mathematica, Tome 136 (1999) no. 1, pp. 71-86

Voir la notice de l'article provenant de la source Institute of Mathematics Polish Academy of Sciences

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.
DOI : 10.4064/sm-136-1-71-86
Keywords: periodically correlated process, stationary process, imprimitivity theorem

Andrzej Makagon 1

1 
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Andrzej Makagon. Induced stationary process and structure of locally square integrable periodically correlated processes. Studia Mathematica, Tome 136 (1999) no. 1, pp. 71-86. doi: 10.4064/sm-136-1-71-86

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