Skip to main content
Log in

On some moments and distributions occurring in the theory of linear stochastic processes. — I

  • Published:
Monatshefte für Mathematik Aims and scope Submit manuscript

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. M. S. Bartlett andP. H. Diananda, “Extensions of Quenouille's test for autoregressive schemes”, J. Roy. Statist. Soc., Ser. B., Vol. 12 (1950), pp. 108–115.

    Google Scholar 

  2. M. S. Bartlett, An Introduction to Stochastic Processes with Special Reference to Methods and Applications, Cambridge University Press, 1955.

  3. H. Cramér, Mathematical Methods of Statistics, Princeton University Press, 1946.

  4. H. Cramér andH. Wold, “Some theorems on distribution functions”, J. London. Math. Soc., Vol.11 (1936), pp. 290–294.

    Google Scholar 

  5. P. H. Diananda, “Some probability limit theorems with statistical applications”, Proc. Cambridge Philos. Soc., Vol. 49 (1953), pp. 239–246.

    Google Scholar 

  6. M. Fréchet andJ. Shohat, “A proof of the generalized second-limit theorem”, Trans. Amer. Math. Soc., Vol. 33 (1931), pp. 533–543.

    Google Scholar 

  7. U. Grenander, “On empirical spectral analysis of stochastic processes”, Ark. Mat., Vol 1 (1951), pp. 503–531.

    Google Scholar 

  8. U. Grenander andM. Rosenblatt, “Statistical spectral analysis of time series arising from stationary stochastic processes”, Ann. Math. Stat., Vol. 24 (1953), pp. 537–558.

    Google Scholar 

  9. U. Grenander andM. Rosenblatt, “Comments on statistical spectral analysis”, Skand. Aktuarietidskr., Vol. 36 (1953), pp. 182–202.

    Google Scholar 

  10. W. Hoeffding andH. Robbins, “The central limit theorem for dependent random variables”, Duke Math. J., Vol. 15 (1948), pp. 773–780.

    Google Scholar 

  11. M. Kendall, The Advanced Theory of Statistics, Vol. I, Charles Griffin & Co., New York and London, 1945.

    Google Scholar 

  12. P. Lévy, Théorie de l'Addition des Variables Aléatoires, Gauthier-Villars, Paris, 1937.

    Google Scholar 

  13. M. Loève, Probability Theory. Foundations. Random Sequence. D. van Nostrand Co., New York, 1955.

    Google Scholar 

  14. Z. A. Lomnicki andS. K. Zaremba, “On the estimation of autocorrelation in time series”, Ann. Math. Stat., Vol. 28 (1957), pp. 140–158.

    Google Scholar 

  15. Z. A. Lomnicki andS. K. Zaremba, “On estimating the spectral density function of a stochastic process”, J. Roy. Statist. Soc. (in print).

  16. Z. A. Lomnicki andS. K. Zaremba, “A further instance of the central limit theorem for dependent random variables”, Math. Zeitschr., Vol. 66 (1957), pp. 490–494.

    Google Scholar 

  17. H. B. Mann andA. Wald, “On the statistical treatment of linear stochastic difference equations”, Econometrica, Vol. 11 (1943), pp. 173–220.

    Google Scholar 

  18. C. Marsaglia, “Iterated limits and the central limit theorem for dependent variables”, Proc. Amer. Math. Soc., Vol. 5 (1954), pp. 987–991.

    Google Scholar 

  19. P. A. P. Moran, “Some theorems on time series, I”, Biometrika, Vol. 34 (1947), pp. 281–291.

    Google Scholar 

  20. M. H. Quenouille, “A large-sample test for the goodness of fit of autoregressive schemes”, J. Roy. Statist. Soc., Vol. 110 (1947), pp. 123–129.

    Google Scholar 

  21. J. V. Uspensky, Introduction to Mathematical Probability, McGraw-Hill Book Co., New York and London, 1937.

    Google Scholar 

Download references

Author information

Authors and Affiliations

Authors

Rights and permissions

Reprints and permissions

About this article

Cite this article

Lomnicki, Z.A., Zaremba, S.K. On some moments and distributions occurring in the theory of linear stochastic processes. — I. Monatshefte für Mathematik 61, 318–358 (1957). https://doi.org/10.1007/BF01305937

Download citation

  • Received:

  • Issue Date:

  • DOI: https://doi.org/10.1007/BF01305937

Keywords

Navigation