Advertisement

Acta Mathematica

, Volume 99, Issue 1, pp 93–137 | Cite as

The prediction theory of multivariate stochastic processes, II

The linear predictor
  • N. Wiener
  • P. Masani
Article

Keywords

Spectral Density Fourier Coefficient Correlation Matrice Prediction Problem Linear Predictor 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  1. [1].
    G. D. Birkhoff, Proof of the ergodic theorem.Proc. Nat. Acad. Sci. U.S.A., 17 (1931), 656–660.zbMATHCrossRefGoogle Scholar
  2. [2].
    H. W. Bode &C. E. Shannon, Linear least square smoothing and prediction theory.Proc. Inst. Radio Engineers, 38 (1950), 417–425.MathSciNetGoogle Scholar
  3. [3].
    H. Cramér, On the theory of stationary random processes.Ann. of Math., 41 (1940), 215–230.CrossRefMathSciNetGoogle Scholar
  4. [4].
    J. L. Doob,Stochastic Processes. New York, (1953).Google Scholar
  5. [5].
    A. Kolmogorov, Stationary sequences in Hilbert space. (Russian.)Bull. Math. Univ., Moscou, 2, No. 6 (1941), 40 pp. (English translation by Natasha Artin.)Google Scholar
  6. [6].
    P. Masani, The Laurent factorization of operator-valued functions.Proc. London Math. Soc., 6 (1956), 59–69.zbMATHCrossRefMathSciNetGoogle Scholar
  7. [7].
    J. C. Oxtoby &S. M. Ulam, Measure-preserving homeomorphims and metrical transitivity.Ann. of Math., 42 (1941), 874–920.CrossRefMathSciNetGoogle Scholar
  8. [8].
    J. von Neummann, Zur Operatorenmethode in der klassischen Mechanik.Ann. of Math., 33 (1932), 587–642.CrossRefMathSciNetGoogle Scholar
  9. [9].
    J. von Neummann,Functional Operators, vol. II. Princeton (1950).Google Scholar
  10. [10].
    N. Wiener,The Extrapolation, Interpolation and Smoothing of Stationary Time Series. New York (1950).Google Scholar
  11. [11].
    —, On the factorization of matrices.Comment. Math. Helv., 29 (1955), 97–111.zbMATHCrossRefMathSciNetGoogle Scholar
  12. [12].
    N. Wiener &P. Masani, The prediction theory of multivariate stochastic processes, Part I.Acta Math., 98 (1957), 111–150.CrossRefMathSciNetGoogle Scholar

Copyright information

© Almqvist & Wiksells Boktryckeri AB 1958

Authors and Affiliations

  • N. Wiener
    • 1
    • 2
  • P. Masani
    • 1
    • 2
  1. 1.CambridgeUSA
  2. 2.BombayIndia

Personalised recommendations