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

Andrzej Makagon

Studia Mathematica (1999)

  • Volume: 136, Issue: 1, page 71-86
  • ISSN: 0039-3223

Abstract

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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 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.

How to cite

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Makagon, Andrzej. "Induced stationary process and structure of locally square integrable periodically correlated processes." Studia Mathematica 136.1 (1999): 71-86. <http://eudml.org/doc/216661>.

@article{Makagon1999,
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.},
author = {Makagon, Andrzej},
journal = {Studia Mathematica},
keywords = {periodically correlated process; stationary process; imprimitivity theorem},
language = {eng},
number = {1},
pages = {71-86},
title = {Induced stationary process and structure of locally square integrable periodically correlated processes},
url = {http://eudml.org/doc/216661},
volume = {136},
year = {1999},
}

TY - JOUR
AU - Makagon, Andrzej
TI - Induced stationary process and structure of locally square integrable periodically correlated processes
JO - Studia Mathematica
PY - 1999
VL - 136
IS - 1
SP - 71
EP - 86
AB - 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.
LA - eng
KW - periodically correlated process; stationary process; imprimitivity theorem
UR - http://eudml.org/doc/216661
ER -

References

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  11. [11] A. Makagon, A. G. Miamee and H. Salehi, Continuous time periodically correlated processes; spectrum and prediction, Stochastic Process. Appl. 49 (1994), 277-295. Zbl0791.60031
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