Previous |  Up |  Next


Wold decomposition; stationary process; Lebesgue decomposition; spectral measure
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.
[1] P. R. Halmos: Shifts on Hilbert spaces. J. reine angew. Math., 208 (1961), 102-112. MR 0152896 | Zbl 0107.09802
[2] H. Helson: Lectures on invariant subspaces. Academic Press, New York-London, 1964. MR 0171178 | Zbl 0119.11303
[3] N. K. Nikoľskij: Lectures on shift operator. (Russian), Nauka, Moskva, 1980. MR 0575166
[4] Ju. A. Rozanov: Stationary stochastic processes. (Russian), Fizmatgiz, Moskva, 1963. MR 0159363
[5] B. Szökefalvi-Nagy C. Foiaş: Harmonic analysis of operators on Hilbert space. Académiai Kiadó, Budapest, 1970. MR 0275190
[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. DOI 10.1007/BF02404472
[7] H. Wold: A study in the analysis of stationary time series. Almquist and Wiksells, Uppsala, 1938. MR 0061344 | Zbl 0019.35602
Partner of
EuDML logo