Skip to main content
SpringerLink
Log in

Normalized convergence of random variables

  • Systems Analysis
  • Published:
Cybernetics and Systems Analysis Aims and scope

Abstract

The properties of a new type of convergence of sequences of random variables are considered. Normalized convergence occupies an intermediate position between convergence in the mean and convergence in probability. It is relevant for studying the rate of convergence of stochastic iterative optimization algorithms and statistical methods of stochastic programming.

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

Similar content being viewed by others

References

  1. Yu. M. Ermoliev and V. I. Norkin, Normalized Convergence in Stochastic Optimization, Preprint WP-89-091, IIASA, Laxenburg, Austria (1989).

    Google Scholar 

  2. V. I. Norkin, Stability of Stochastic Optimization Models and Statistical Methods of Stochastic Programming [in Russian], Preprint 89-53, Inst. Kiber. im. V. M. Glushkova AN UkrSSR, Kiev (1989).

    Google Scholar 

  3. Yu. M. Ermol'ev and V. I. Norkin, “Normalized convergence of random variables and its application,” Kibernetika, No. 6, 89–93 (1990).

    Google Scholar 

  4. V. I. Norkin, “On conditions and rate of convergence of the empirical mean method in mathematical statistics and stochastic programming,” Kibernetika, No. 2, 107–120 (1992).

    Google Scholar 

  5. V. G. Karmanov, Mathematical Programming [in Russian], Nauka, Moscow (1975).

    Google Scholar 

  6. B. T. Polyak, “Convergence and rate of convergence of iterative stochastic algorithms. I. General case,” Avtomat. Telemekh., No. 12, 83–94 (1976).

    Google Scholar 

  7. M. V. Mikhalevich, “Rate of convergence bounds for a method of searching for the best element,” Zh. Vychisl. Mat. Mat. Fiz.,26, No. 7, 994–1005 (1986).

    Google Scholar 

  8. A. V. Tsibakov, “Accuracy estimates for the empirical risk method,” Prob. Peredachi Inform.,17, No. 1, 50–61 (1981).

    Google Scholar 

  9. P. Billingsley, Convergence of Probability Measures, Wiley, New York (1968).

    Google Scholar 

  10. R. Ranga Rao, “Relations between weak and uniform convergence of measures with applications,” Ann. Math. Stat.,33, 659–680 (1962).

    Google Scholar 

Download references

Authors
  1. V. I. Norkin
    View author publications

    You can also search for this author in PubMed Google Scholar

Additional information

Translated from Kibernetika i Sistemnyi Analiz, No. 3, pp. 84–92, May–June, 1992.

Rights and permissions

Reprints and permissions

About this article

Cite this article

Norkin, V.I. Normalized convergence of random variables. Cybern Syst Anal 28, 396–402 (1992). https://doi.org/10.1007/BF01125420

Download citation

  • Received:

  • Issue Date:

  • DOI: https://doi.org/10.1007/BF01125420

Keywords

Search

Navigation