Skip to main content
Log in

The prediction theory of multivariate stochastic processes, III

Unbounded spectral densities

  • Published:
Acta Mathematica

This is a preview of subscription content, log in via an institution to check access.

Access this article

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

References

  1. E. J. Akutowicz, On an explicit formula in linear least squares prediction.Math. Scand., 5 (1957), 261–266.

    MATH  MathSciNet  Google Scholar 

  2. A. N. Kolmogorov, Stationary sequences in Hilbert space (Russian).Bull. Math. Univ. Moscou, 2, No. 6 (1941) 40 pp. (English translation by Natasha Artin).

  3. P. Masani, Sur les processus vectoriels minimaux de rang maximal.C. R. Acad. Sci. Paris, 246 (1958), 2215–2217.

    MATH  MathSciNet  Google Scholar 

  4. —, Sur la prévision linéaire d’un processus vectoriel à densité spectrale non bornée,C. R. Acad. Sci. Paris, 246 (1958), 2337–2339.

    MATH  MathSciNet  Google Scholar 

  5. P. Masani &N. Wiener, On bivariate stationary processes and the factorization of matrix-valued functions.Teoria veroyatnosti i ee primenenie (Moscow), IV (1959), 322–331.

    MathSciNet  Google Scholar 

  6. IU. A. Rosanov, Spectral theory of multidimensional stationary random processes with discrete time (Russian).Uspehi Math. Nauk, XIII, No. 2 (1958), 93–142.

    Google Scholar 

  7. N. Wiener,The grammar of the semi-exact sciences (lectures edited by G. Kallianpur); mimeographed, Indian Statistical Institute, Calcutta (1956).

    Google Scholar 

  8. N. Wiener &P. Masani, The prediction theory of multivariate stochastic processes, Part I.Acta Math., 98 (1957), 111–150, Part II,Acta Math., 99 (1958), 93–137.

    Article  MathSciNet  Google Scholar 

  9. V. Zasuhin, On the theory of multidimensional stationary random processes (Russian).C. R. (Doklady) Acad Sci. U.R.S.S., 33 (1941), 435.

    MathSciNet  Google Scholar 

Download references

Author information

Authors and Affiliations

Authors

Additional information

The writer wishes to thank Harvard University and the Massachusetts Institute of Technology for visting appointments in 1957–58, during which a part of this research was completed.

Rights and permissions

Reprints and permissions

About this article

Cite this article

Masani, P. The prediction theory of multivariate stochastic processes, III. Acta Math. 104, 141–162 (1960). https://doi.org/10.1007/BF02547188

Download citation

  • Received:

  • Issue Date:

  • DOI: https://doi.org/10.1007/BF02547188

Keywords

Navigation