Skip to main content
SpringerLink
Log in

On One-Sided Convergence of a Modified Stochastic Approximation Process

  • Stochastic Systems
  • Published:
Automation and Remote Control Aims and scope Submit manuscript

Abstract

We study the one-sided convergence of the modified Anbar’s process in previously unexplored cases of the choice of the sequence of steps.

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. Anbar, D., A Modified Robbins–Monro Procedure Approximating the Zero of a Regression from Below, Ann. Statist., 1977, vol. 5, no. 1, pp. 229–234.

    Article  MathSciNet  MATH  Google Scholar 

  2. Gaposhkin, V.F. and Krasulina, T.P., On the Repeated Logarithm Law in Stochastic Approximation Processes, Teor. Veroyat. Primen., 1974, vol. 19, no. 4, pp. 879–886.

    Google Scholar 

  3. Doob, J.L., Stochastic Processes, New York: Wiley, 1953. Translated under the title Veroyatnostnye protsessy, Moscow: Inostrannaya Literatura, 1956.

    Google Scholar 

  4. Loeve, M., Probability Theory, New York: Springer, 1977. Translated under the title Teoriya veroyatnostei, Moscow: Inostrannaya Literatura, 1962.

    MATH  Google Scholar 

  5. Gladyshev, E.G., On Stochastic Approximation, Teor. Veroyat. Primen., 1965, vol. 10, no. 2, pp. 297–300.

    Google Scholar 

  6. Nevel’son, M.B. and Khas’minskii, R.Z., Stokhasticheskaya approksimatsiya i rekurrentnoe otsenivanie (Stochastic Approximation and Recurrent Estimation), Moscow: Nauka, 1972.

    Google Scholar 

  7. Krasulina, T.P., Finding Fixed Points of Functions with Stochastic Approximation Methods, Vestn. S.-Peterburg. Gos. Univ., Ser. 1, 2017, no. 1, pp. 22–24.

    MathSciNet  Google Scholar 

Download references

Author information

Authors and Affiliations

  1. St. Petersburg State University, St. Petersburg, Russia

    T. P. Krasulina

Authors
  1. T. P. Krasulina
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to T. P. Krasulina.

Additional information

Original Russian Text © T.P. Krasulina, 2018, published in Avtomatika i Telemekhanika, 2018, No. 2, pp. 106–108.

Rights and permissions

Reprints and permissions

About this article

Check for updates. Verify currency and authenticity via CrossMark

Cite this article

Krasulina, T.P. On One-Sided Convergence of a Modified Stochastic Approximation Process. Autom Remote Control 79, 286–288 (2018). https://doi.org/10.1134/S0005117918020078

Download citation

  • Received:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1134/S0005117918020078

Keywords

Search

Navigation