Advertisement

Siberian Mathematical Journal

, Volume 20, Issue 5, pp 691–699 | Cite as

Estimates of means for almost all realizations of stationary processes

  • V. F. Gaposhkin
Article

Keywords

Stationary Process 
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.

Literature Cited

  1. 1.
    M. Loeve, Probability Theory, Springer-Verlag (1977).Google Scholar
  2. 2.
    I. N. Verbitskaya, “On conditions for applicability of the strong law of large numbers to processes stationary in the extended sense,” Teor. Veroyatn. Ee Primen.,11, No. 4, 715–719 (1966).Google Scholar
  3. 3.
    V. V. Petrov, “On the strong law of large numbers for a stationary sequence,” Dokl. Akad. Nauk SSSR,213, No. 1, 42–44 (1973).Google Scholar
  4. 4.
    V. F. Gaposhkin, “Convergence of series related to stationary sequences,” Izv. Akad. Nauk SSSR, Ser. Mat.,39, No. 6, 1366–1392 (1975).Google Scholar
  5. 5.
    V. F. Gaposhkin, “Criteria for the strong law of large numbers for classes of stationary processes and homogeneous stochastic fields,” Teor. Veroyatn. Ee Primen.,22, No. 2, 296–319 (1977).Google Scholar
  6. 6.
    V. F. Gaposhkin, “Precise estimates of rate of convergence in the strong law of large numbers for classes of sequences and processes stationary in the extended sense,” Usp. Mat. Nauk,31, No. 5, 233–234 (1976).Google Scholar
  7. 7.
    A. Arimoto, “Notes on the strong law of large numbers for a weakly stationary stochastic process,” Repts. Stat., Appl. Res. Union Jpn. Sci. Eng.,22, No. 4, 164–167 (1975).Google Scholar
  8. 8.
    R. J. Serfling, “Convergence properties of Sn under moment restrictions,” Ann. Math. Stat.,41, No. 4, 1235–1248 (1970).Google Scholar
  9. 9.
    F. Moricz, “A generalization of some classical inequalities in the theory of orthogonal series,” Mat. Zametki,17, No. 2, 219–230 (1975).Google Scholar
  10. 10.
    F. Moricz, “Moment inequalities and the strong law of large numbers,” Z. Wahrschein.,35, No. 4, 299–314 (1976).Google Scholar
  11. 11.
    G. Aleksich, Problems in the Convergence of Orthogonal Series [Russian translation], IL, Moscow (1964).Google Scholar
  12. 12.
    A. Zygmund, Trigonometric Series, Cambridge Univ. Press (1968).Google Scholar
  13. 13.
    P. Sjölin, “Convergence almost everywhere of certain singular integrals and multiple Fourier series,” Ark. Math.,9, No. 1, 65–90 (1971).Google Scholar

Copyright information

© Plenum Publishing Corporation 1980

Authors and Affiliations

  • V. F. Gaposhkin

There are no affiliations available

Personalised recommendations