Skip to main content
SpringerLink
Log in

The order of approximation in the central limit theorem for random summation

  • Published:
Acta Mathematica Hungarica 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

References

  1. F. J. Anscombe, Large-sample theory of sequential estimation,Proc. Cambridge Philos. Soc.,48 (1952), 600–607.

    Google Scholar 

  2. G. J. Babu, M. Ghosh, A random functional central limit theorem for martingales,Acta Math. Acad. Sci. Hung.,27 (1976), 301–306.

    Google Scholar 

  3. J. R. Blum, D. I. Hanson, J. I. Rosenblatt, On the central limit theorem for the sum of a random number of independent random variables,Z. Wahr. verw. Geb.,1 (1963), 389–393.

    Google Scholar 

  4. H. Callaert, P. Janssen, A note on the convergence rate of random sums,Rev. Roum. Math. Pures et Appl.,28 (1983), 147–151.

    Google Scholar 

  5. M. Csörgő, Z. Rychlik, Weak convergence of sequences of random elements with random indices,Math. Proc. Camb. Phil. Soc.,88 (1980), 171–174.

    Google Scholar 

  6. Б. В. Гнеденко, О свя зи теории суммирован ия независимых случа йных величин с задача ми теории масового об служивания и теории н адежности,Rev. Roum. Math. Pures et Appl.,9 (1967), 1243–1253.

    Google Scholar 

  7. P. Hall, C. C. Heyde,Martingale Limit Theory and Its Application, Academic Press (New York, 1980).

    Google Scholar 

  8. D. Landers, L. Rogge, A counterexample in the approximation theory of random summation.The Annals of Probab.,5 (1977), 1018–1023.

    Google Scholar 

  9. D. Landers, L. Rogge, The exact approximation order in the central-limit-theorem for random summation,Z. Wahr. verw. Geb.,36 (1976), 269–283.

    Google Scholar 

  10. J. Mogyoródi, A central limit theorem for the sum of a random number of independent random variables,Publ. Math. Inst. Hungar. Acad. Sci. Ser. A,7 (1962), 409–424.

    Google Scholar 

  11. В. В.Петров,Суммы нез ависимых случайных в еличин, Издат. «Наука» (Москва, 1972).

  12. A. Rényi, On the central limit theorem for the sum of a random number of independent random variables,Acta Math. Acad. Sci. Hungar.,11 (1960), 97–102.

    Google Scholar 

  13. Z. Rychlik, The order of approximation in the random central limit theorem,Lect. Notes in Math., Vol.656 (1978), 225–236.

    Google Scholar 

  14. E. Schneider, On the speed of convergence in the random central limit theorem forϕ-mixing processes,Z. Wahr. verw. Geb.,58 (1981), 125–138.

    Google Scholar 

Download references

Author information

Authors and Affiliations

  1. Institute of Mathematics, Maria Curie-Skłodowska Universit, Ul. Nowotki 10, 20-031, Lublin, Poland

    A. Krajka & Z. Rychlik

Authors
  1. A. Krajka
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Z. Rychlik
    View author publications

    You can also search for this author in PubMed Google Scholar

Rights and permissions

Reprints and permissions

About this article

Cite this article

Krajka, A., Rychlik, Z. The order of approximation in the central limit theorem for random summation. Acta Math Hung 51, 109–115 (1988). https://doi.org/10.1007/BF01903624

Download citation

  • Received:

  • Issue Date:

  • DOI: https://doi.org/10.1007/BF01903624

Keywords

Search

Navigation