A remark concerning uniqueness of the Wold decomposition of finite-dimensional stationary processes.
Horák, Karel ; Müller, Vladimír ; Vrbová, Pavla
Applications of Mathematics, Tome 32 (1987), p. 337-345 / Harvested from Czech Digital Mathematics Library

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.

Publié le : 1987-01-01
Classification:  47A15,  47B15,  60G10,  60G25
@article{104265,
     author = {Karel Hor\'ak and Vladim\'\i r M\"uller and Pavla Vrbov\'a},
     title = {A remark concerning uniqueness of the Wold decomposition of finite-dimensional stationary processes.},
     journal = {Applications of Mathematics},
     volume = {32},
     year = {1987},
     pages = {337-345},
     zbl = {0645.60043},
     mrnumber = {0909541},
     language = {en},
     url = {http://dml.mathdoc.fr/item/104265}
}
Horák, Karel; Müller, Vladimír; Vrbová, Pavla. A remark concerning uniqueness of the Wold decomposition of finite-dimensional stationary processes.. Applications of Mathematics, Tome 32 (1987) pp. 337-345. http://gdmltest.u-ga.fr/item/104265/

P. R. Halmos Shifts on Hilbert spaces, J. reine angew. Math., 208 (1961), 102-112. (1961) | MR 0152896 | Zbl 0107.09802

H. Helson Lectures on invariant subspaces, Academic Press, New York-London, 1964. (1964) | MR 0171178 | Zbl 0119.11303

N. K. Nikoľskij Lectures on shift operator, (Russian), Nauka, Moskva, 1980. (1980) | MR 0575166

Ju. A. Rozanov Stationary stochastic processes, (Russian), Fizmatgiz, Moskva, 1963. (1963) | MR 0159363

B. Szökefalvi-Nagy C. Foiaş Harmonic analysis of operators on Hilbert space, Académiai Kiadó, Budapest, 1970. (1970) | MR 0275190

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. (1957) | Article

H. Wold A study in the analysis of stationary time series, Almquist and Wiksells, Uppsala, 1938. (1938) | MR 0061344 | Zbl 0019.35602