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.
@article{bwmeta1.element.bwnjournal-article-smv136i1p71bwm,
author = {Andrzej Makagon},
title = {Induced stationary process and structure of locally square integrable periodically correlated processes},
journal = {Studia Mathematica},
volume = {133},
year = {1999},
pages = {71-86},
zbl = {0947.60032},
language = {en},
url = {http://dml.mathdoc.fr/item/bwmeta1.element.bwnjournal-article-smv136i1p71bwm}
}
Makagon, Andrzej. Induced stationary process and structure of locally square integrable periodically correlated processes. Studia Mathematica, Tome 133 (1999) pp. 71-86. http://gdmltest.u-ga.fr/item/bwmeta1.element.bwnjournal-article-smv136i1p71bwm/
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