A remark concerning uniqueness of the Wold decomposition of finite-dimensional stationary processes.

Karel Horák; Vladimír Müller; Pavla Vrbová

Aplikace matematiky (1987)

  • Volume: 32, Issue: 5, page 337-345
  • ISSN: 0862-7940

Abstract

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The uniqueness of the Wold decomposition of a finite-dimensional stationary process without assumption of full rank stationary process and the Lebesgue decomposition of its spectral measure is easily obtained.

How to cite

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Horák, Karel, Müller, Vladimír, and Vrbová, Pavla. "A remark concerning uniqueness of the Wold decomposition of finite-dimensional stationary processes.." Aplikace matematiky 32.5 (1987): 337-345. <http://eudml.org/doc/15505>.

@article{Horák1987,
abstract = {The uniqueness of the Wold decomposition of a finite-dimensional stationary process without assumption of full rank stationary process and the Lebesgue decomposition of its spectral measure is easily obtained.},
author = {Horák, Karel, Müller, Vladimír, Vrbová, Pavla},
journal = {Aplikace matematiky},
keywords = {Wold decomposition; stationary process; Lebesgue decomposition; spectral measure; Wold decomposition; stationary process; Lebesgue decomposition; spectral measure},
language = {eng},
number = {5},
pages = {337-345},
publisher = {Institute of Mathematics, Academy of Sciences of the Czech Republic},
title = {A remark concerning uniqueness of the Wold decomposition of finite-dimensional stationary processes.},
url = {http://eudml.org/doc/15505},
volume = {32},
year = {1987},
}

TY - JOUR
AU - Horák, Karel
AU - Müller, Vladimír
AU - Vrbová, Pavla
TI - A remark concerning uniqueness of the Wold decomposition of finite-dimensional stationary processes.
JO - Aplikace matematiky
PY - 1987
PB - Institute of Mathematics, Academy of Sciences of the Czech Republic
VL - 32
IS - 5
SP - 337
EP - 345
AB - The uniqueness of the Wold decomposition of a finite-dimensional stationary process without assumption of full rank stationary process and the Lebesgue decomposition of its spectral measure is easily obtained.
LA - eng
KW - Wold decomposition; stationary process; Lebesgue decomposition; spectral measure; Wold decomposition; stationary process; Lebesgue decomposition; spectral measure
UR - http://eudml.org/doc/15505
ER -

References

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  1. P. R. Halmos, Shifts on Hilbert spaces, J. reine angew. Math., 208 (1961), 102-112. (1961) Zbl0107.09802MR0152896
  2. H. Helson, Lectures on invariant subspaces, Academic Press, New York-London, 1964. (1964) Zbl0119.11303MR0171178
  3. N. K. Nikoľskij, Lectures on shift operator, (Russian), Nauka, Moskva, 1980. (1980) MR0575166
  4. Ju. A. Rozanov, Stationary stochastic processes, (Russian), Fizmatgiz, Moskva, 1963. (1963) Zbl0121.12602MR0159363
  5. B. Szökefalvi-Nagy C. Foiaş, Harmonic analysis of operators on Hilbert space, Académiai Kiadó, Budapest, 1970. (1970) Zbl0201.45003MR0275190
  6. N. Wiener P. Masani, 10.1007/BF02404472, Acta Math., 98 (1957), 111-150; II, Acta Math., 99 (1958), 93-137. (1957) Zbl0080.13002DOI10.1007/BF02404472
  7. H. Wold, A study in the analysis of stationary time series, Almquist and Wiksells, Uppsala, 1938. (1938) Zbl0019.35602MR0061344

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