| Title:
|
A remark concerning uniqueness of the Wold decomposition of finite-dimensional stationary processes. (English) |
| Author:
|
Horák, Karel |
| Author:
|
Müller, Vladimír |
| Author:
|
Vrbová, Pavla |
| Language:
|
English |
| Journal:
|
Aplikace matematiky |
| ISSN:
|
0373-6725 |
| Volume:
|
32 |
| Issue:
|
5 |
| Year:
|
1987 |
| Pages:
|
337-345 |
| Summary lang:
|
English |
| Summary lang:
|
Russian |
| Summary lang:
|
Czech |
| . |
| Category:
|
math |
| . |
| Summary:
|
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. (English) |
| Keyword:
|
Wold decomposition |
| Keyword:
|
stationary process |
| Keyword:
|
Lebesgue decomposition |
| Keyword:
|
spectral measure |
| MSC:
|
47A15 |
| MSC:
|
47B15 |
| MSC:
|
60G10 |
| MSC:
|
60G25 |
| idZBL:
|
Zbl 0645.60043 |
| idMR:
|
MR0909541 |
| DOI:
|
10.21136/AM.1987.104265 |
| . |
| Date available:
|
2008-05-20T18:32:55Z |
| Last updated:
|
2020-07-28 |
| Stable URL:
|
http://hdl.handle.net/10338.dmlcz/104265 |
| . |
| Reference:
|
[1] P. R. Halmos: Shifts on Hilbert spaces.J. reine angew. Math., 208 (1961), 102-112. Zbl 0107.09802, MR 0152896 |
| Reference:
|
[2] H. Helson: Lectures on invariant subspaces.Academic Press, New York-London, 1964. Zbl 0119.11303, MR 0171178 |
| Reference:
|
[3] N. K. Nikoľskij: Lectures on shift operator.(Russian), Nauka, Moskva, 1980. MR 0575166 |
| Reference:
|
[4] Ju. A. Rozanov: Stationary stochastic processes.(Russian), Fizmatgiz, Moskva, 1963. MR 0159363 |
| Reference:
|
[5] B. Szökefalvi-Nagy C. Foiaş: Harmonic analysis of operators on Hilbert space.Académiai Kiadó, Budapest, 1970. MR 0275190 |
| Reference:
|
[6] N. Wiener P. Masani: The prediction theory of multivariate stochastic processes I.Acta Math., 98 (1957), 111-150; II, Acta Math., 99 (1958), 93-137. 10.1007/BF02404472 |
| Reference:
|
[7] H. Wold: A study in the analysis of stationary time series.Almquist and Wiksells, Uppsala, 1938. Zbl 0019.35602, MR 0061344 |
| . |
