Skip to main content
SpringerLink
Log in

Limit theorems for processes generated by stochastic optimization algorithms

  • Section II Stochastic Extremal Problems
  • Conference paper
  • First Online:
Stochastic Optimization

Part of the book series: Lecture Notes in Control and Information Sciences ((LNCIS,volume 81))

  • 128 Accesses

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

Access this chapter

Log in via an institution

Institutional subscriptions

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  1. I.I. Gihman. Limit theorems for triangular arrays of random variables (in Russian). In Theor. Slutchaynyh Prosessov, Vol. 2, 1974, p. 37–47.

    Google Scholar 

  2. I.I. Gihman and A.V. Skorohod. The Theory of Random Processes, Vol. 3, Wiley, New York, 1978.

    Google Scholar 

  3. V.V. Anisimov and Z.P. Anisimova. On the convergence of random processes generated by a procedure of the Robbins-Monro type (in Russian). In Analytical Methods in Probability Theory, p. 104–108. Naukova Dumka, Kiev, 1979.

    Google Scholar 

  4. V.V. Anisimov. On the convergence of multivariate inhomogeneous stochastic approximation procedures (in Russian). Doklady Akademii Nauk Ukrainskoj SSR, 5(1981) 82–85.

    Google Scholar 

  5. V.V. Anisimov. Limit theorems for random processes generated by stochastic approximation procedures (in Russian). In Vychislit. i Pricl. Matematika, Vol. 46, p. 32–41, Kiev, 1982.

    Google Scholar 

  6. D. McLeish. Functional and random limit theorems for the Robbins-Monro process. Journal of Applied Probability, 13(1)(1976)148–154.

    Google Scholar 

  7. V.V. Anisimov and A.P. Yurachkovsky. A limit theorem for stochastic difference schemes with random coefficients (in Russian). In Teoriya Veroyatnosti i Matematicheskaya Statistika, Vol. 33, 1985.

    Google Scholar 

  8. I.I. Gihman and A.V. Skorohod. Stochastic Differential Equations and their Applications. Naukova Dumka, Kiev, 1982 (in Russian).

    Google Scholar 

  9. R.Sh. Liptser and A.N. Shyryaev. Weak convergence of a sequence of semimartingales to a diffusion-type process (in Russian). In Matematecheskie Sbornik, 121(2)(1983)176–204.

    Google Scholar 

  10. M.B. Nevelson and R.Z. Hasminskiy. Stochastic Approximation and Recursive Estimation. Nauka, Moscow, 1972 (in Russian).

    Google Scholar 

  11. I.I. Gihman and A.V. Skorohod. Stochastic Differential Equations. Naukova Dumka, Kiev, 1968 (in Russian).

    Google Scholar 

  12. R.Z. Hasminskiy. Stability of Systems of Differential Equations with Randomly Perturbed Parameters. Nauka, Moscow, 1969 (in Russian).

    Google Scholar 

  13. R.Z. Hasminskiy. Convergence of processes generated by multivariate stochastic optimization procedures (in Russian). In Teoriya Veroyatnosti i Matematicheskaya Statistika, Vol. 33, 1985.

    Google Scholar 

Download references

Author information

Authors and Affiliations

  1. Kiev State University, Kiev, USSR

    V. V. Anisimov

Authors
  1. V. V. Anisimov
    View author publications

    You can also search for this author in PubMed Google Scholar

Editor information

Vadim I. Arkin A. Shiraev R. Wets

Rights and permissions

Reprints and permissions

Copyright information

© 1986 International Institute for Applied Systems Analysis

About this paper

Cite this paper

Anisimov, V.V. (1986). Limit theorems for processes generated by stochastic optimization algorithms. In: Arkin, V.I., Shiraev, A., Wets, R. (eds) Stochastic Optimization. Lecture Notes in Control and Information Sciences, vol 81. Springer, Berlin, Heidelberg. https://doi.org/10.1007/BFb0007103

Download citation

  • DOI: https://doi.org/10.1007/BFb0007103

  • Published:

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-16659-7

  • Online ISBN: 978-3-540-39841-7

  • eBook Packages: Springer Book Archive

Publish with us

Policies and ethics

Search

Navigation