A duality principle for stationary random sequences

K. Urbanik

Colloquium Mathematicae (2000)

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

Abstract

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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.

How to cite

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Urbanik, 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

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  1. [1] J. L. Doob, Stochastic Processes, Wiley, New York, 1953. Zbl0053.26802
  2. [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. [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. [4] I. I. Privalov, Limit Properties of Analytic Functions, G.I.T.-T.L., Moscow, 1950 (in Russian). 
  5. [5] Yu. A. Rozanov, Stationary Random Processes, G.I.F.-M.L., Moscow, 1963 (in Russian). 
  6. [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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