Skip to main content
SpringerLink
Log in

A refinement of the error estimate of the normal approximation in a Hilbert space

  • Published:
Siberian Mathematical Journal Aims and scope Submit manuscript

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

Access this article

Log in via an institution

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

Instant access to the full article PDF.

Institutional subscriptions

Literature Cited

  1. B. A. Zalesskii, “Estimates of the accuracy of normal approximation in Hilbert space,” Teor. Veroyatn. Primen.,27, No. 2, 279–285 (1982).

    Google Scholar 

  2. V. Yu. Bentkus, “Asymptotic expansions for sums of independent random elements in a Hilbert space,” Dokl. Akad. Nauk SSSR,278, No. 5, 1033–1036 (1984).

    Google Scholar 

  3. C.-G. Esseen, “Fourier analysis of distribution functions. A mathematical study of the Laplace-Gaussian law,” Acta Math.,77, 1–125 (1945).

    Google Scholar 

  4. I. F. Pinelis, “Estimates for moments of infinite-dimensional martingales,” Mat. Zametki,27, No. 6, 953–958 (1980).

    Google Scholar 

  5. F. Götze, “Asymptotic expansions for bivariate von Mises functionals” Z. Wahrscheinlichkeitstheorie Verw. Gebiete,50, No. 3, 333–355 (1979).

    Google Scholar 

  6. A. Bikyalis, “On multivariate characteristic functions,” Litov. Mat. Sb. (Liet. Mat. Rinkinys),8, No. 1, 21–39 (1968).

    Google Scholar 

  7. R. N. Bhattacharya and R. Ranga Rao, Normal Approximation and Asymptotic, Expansions, Wiley, New York (1976).

    Google Scholar 

  8. S. V. Nagaev, “On accuracy of normal approximation for distribution of sum of independent Hilbert space valued random variables,” Lect. Notes Math., No. 1021, 461–473 (1983).

    Google Scholar 

  9. I. F. Pinelis, “On the distribution of sums of independent random variables with values in a Banach space,”, Teor. Veroyatn. Primen.,23, No. 3, 630–637 (1978).

    Google Scholar 

  10. V. V. Petrov, Sums of Independent Random Variables, Springer-Verlag, New York (1975).

    Google Scholar 

  11. I. A. Ibragimov, “On the probability of a Gaussian vector with values in a Hilbert space hitting a ball of small radius,” J. Sov. Math.,20, No. 3 (1982).

  12. I. I. Gikhman (Gihman) and A. V. Shorokhod (Skorohod), The Theory of Stochastic Processes, I, Springer-Verlag, New York (1974).

    Google Scholar 

  13. V. V. Yurinskii, “On the estimation of the error of normal approximation for the probability of hitting a ball,” Dokl. Akad. Nauk SSSR,258, No. 3, 557–558 (1981).

    Google Scholar 

Download references

Authors
  1. S. V. Nagaev
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. V. I. Chebotarev
    View author publications

    You can also search for this author in PubMed Google Scholar

Additional information

Novosibirsk. Translated from Sibirskii Matematicheskii Zhurnal, Vol. 27, No. 3, pp. 154–173, May–June, 1986.

Rights and permissions

Reprints and permissions

About this article

Cite this article

Nagaev, S.V., Chebotarev, V.I. A refinement of the error estimate of the normal approximation in a Hilbert space. Sib Math J 27, 434–450 (1986). https://doi.org/10.1007/BF00969280

Download citation

  • Received:

  • Issue Date:

  • DOI: https://doi.org/10.1007/BF00969280

Keywords

Search

Navigation