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On the construction of Wold-Cramér decomposition for bivariate stationary processes

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Part of the Lecture Notes in Mathematics book series (LNM,volume 828)

Keywords

  • Spectral Measure
  • Stationary Sequence
  • Complex Hilbert Space
  • Prediction Theory
  • Stationary Stochastic Process

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References

  1. Cramér, H.: On some classes of non-stationary stochastic processes.-Proceedings of the Fourth Berkeley symposium on mathematical statistics and probability, Vol. II, pp. 57–76. University of California Press, Berkeley/Los Angeles, 1962.

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  2. Jang Ze-Pei: The prediction theory of multivariate stationary processes, I.-Chinese Math. 4 (1963), 291–322; II.-Chinese Math. 5 (1964), 471–484.

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  3. Masani, P.: Recent trends in multivariate prediction theory.-Multivariate Analysis I (ed. P.R. Krishnaiah), pp. 351–382. Academic Press, New York/London, 1966.

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  4. Matveev, R.F.: On the regularity of one-dimensional stationary stochastic processes with discrete time.-Dokl.Akad.Nauk. SSSR 25 (1959), 277–280 (In Russian).

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  5. Matveev, R.F.: On singular multidimensional stationary processes.-Theor. Probability Appl. 5 (1960), 33–39.

    CrossRef  Google Scholar 

  6. Matveev, R.F.: On multidimensional regular stationary processes.-Theor. Probability Appl. 6 (1961), 149–165.

    CrossRef  MATH  Google Scholar 

  7. Niemi, H.: On the construction of Wold decomposition for multivariate stationary processes.-J. Multivariate Anal. (to appear).

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  8. Robertson, J.B.: Orthogonal decompositions of multivariate weakly stationary stochastic processes.-Canad. J. Math. 20 (1968), 368–383.

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  9. Wiener, N., and P. Masani: The prediction theory of multivariate stationary processes I.-Acta Math. 98 (1957), 111–150.

    CrossRef  MathSciNet  MATH  Google Scholar 

  10. Wiener, N., and P. Masani: On bivariate stationary processes and the factorization of matrix-valued functions.-Theor. Probability Appl. 4 (1959), 300–308.

    CrossRef  MathSciNet  MATH  Google Scholar 

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© 1980 Springer-Verlag

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Niemi, H. (1980). On the construction of Wold-Cramér decomposition for bivariate stationary processes. In: Weron, A. (eds) Probability Theory on Vector Spaces II. Lecture Notes in Mathematics, vol 828. Springer, Berlin, Heidelberg. https://doi.org/10.1007/BFb0097406

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  • DOI: https://doi.org/10.1007/BFb0097406

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  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-10253-3

  • Online ISBN: 978-3-540-38350-5

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