The paper is devoted to the study of stationary random sequences. A concept of dual sequences is discussed. The main aim of the paper is to establish a relationship between the errors of linear least squares predictions for sequences and their duals.
@article{bwmeta1.element.bwnjournal-article-cmv86i2p153bwm,
author = {K. Urbanik},
title = {A duality principle for stationary random sequences},
journal = {Colloquium Mathematicae},
volume = {84/85},
year = {2000},
pages = {153-162},
language = {en},
url = {http://dml.mathdoc.fr/item/bwmeta1.element.bwnjournal-article-cmv86i2p153bwm}
}
Urbanik, K. A duality principle for stationary random sequences. Colloquium Mathematicae, Tome 84/85 (2000) pp. 153-162. http://gdmltest.u-ga.fr/item/bwmeta1.element.bwnjournal-article-cmv86i2p153bwm/
[00000] [1] J. L. Doob, Stochastic Processes, Wiley, New York, 1953.
[00001] [2] A. N. Kolmogorov, Sur l'interpolation et extrapolation des suites stationnaires, C. R. Acad. Sci. Paris 208 (1939), 2043-2045.
[00002] [3] A. N. Kolmogorov, Interpolation und Extrapolation von stationären zufälligen Folgen, Bull. Acad. Sci. U.R.S.S. Sér. Math. 5 (1941), 3-14.
[00003] [4] I. I. Privalov, Limit Properties of Analytic Functions, G.I.T.-T.L., Moscow, 1950 (in Russian).
[00004] [5] Yu. A. Rozanov, Stationary Random Processes, G.I.F.-M.L., Moscow, 1963 (in Russian).
[00005] [6] N. Wiener, z Extrapolation, Interpolation and Smoothing of Stationary Time Series. With Engineering Applications, The Technology Press of MIT, Cambridge, MA, 1949.