# A duality principle for stationary random sequences

Colloquium Mathematicae (2000)

- Volume: 86, Issue: 2, page 153-162
- ISSN: 0010-1354

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topUrbanik, K.. "A duality principle for stationary random sequences." Colloquium Mathematicae 86.2 (2000): 153-162. <http://eudml.org/doc/210845>.

@article{Urbanik2000,

abstract = {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.},

author = {Urbanik, K.},

journal = {Colloquium Mathematicae},

keywords = {stationary sequence; errors; linear least squares; prediction; dual},

language = {eng},

number = {2},

pages = {153-162},

title = {A duality principle for stationary random sequences},

url = {http://eudml.org/doc/210845},

volume = {86},

year = {2000},

}

TY - JOUR

AU - Urbanik, K.

TI - A duality principle for stationary random sequences

JO - Colloquium Mathematicae

PY - 2000

VL - 86

IS - 2

SP - 153

EP - 162

AB - 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.

LA - eng

KW - stationary sequence; errors; linear least squares; prediction; dual

UR - http://eudml.org/doc/210845

ER -

## References

top- [1] J. L. Doob, Stochastic Processes, Wiley, New York, 1953. Zbl0053.26802
- [2] A. N. Kolmogorov, Sur l'interpolation et extrapolation des suites stationnaires, C. R. Acad. Sci. Paris 208 (1939), 2043-2045. Zbl65.0607.04
- [3] A. N. Kolmogorov, Interpolation und Extrapolation von stationären zufälligen Folgen, Bull. Acad. Sci. U.R.S.S. Sér. Math. 5 (1941), 3-14. Zbl67.0459.02
- [4] I. I. Privalov, Limit Properties of Analytic Functions, G.I.T.-T.L., Moscow, 1950 (in Russian).
- [5] Yu. A. Rozanov, Stationary Random Processes, G.I.F.-M.L., Moscow, 1963 (in Russian).
- [6] N. Wiener, z Extrapolation, Interpolation and Smoothing of Stationary Time Series. With Engineering Applications, The Technology Press of MIT, Cambridge, MA, 1949.

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