Skip to main content
SpringerLink
Log in

On stochastic algorithms in adaptive filtering

  • Conference paper
  • First Online:
Stochastic Processes and Their Applications

Part of the book series: Lecture Notes in Mathematics ((LNM,volume 1203))

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

Access this chapter

Log in via an institution
Chapter
USD 29.95
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
eBook
USD 34.99
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
Softcover Book
USD 46.00
Price excludes VAT (USA)
  • Compact, lightweight edition
  • Dispatched in 3 to 5 business days
  • Free shipping worldwide - see info

Tax calculation will be finalised at checkout

Purchases are for personal use only

Institutional subscriptions

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

Bibliography

  1. A. Benveniste, M. Goursat, G. Ruget, Analysis of stochastic approximation schemes with discontinuous dependent forcing terms. I.E.E.E. Trans. Autom. Control, Vol.AC. 25 no 6 (1980).

    Google Scholar 

  2. C. Bouton, Approximation gaussienne d'Algorithmes sothastiques. These 3 Cycle, Paris VI (1985).

    Google Scholar 

  3. M. Cottrell, J.C. Fort, G. Malgouyres, Large deviations and rare events in the study of stochastic algorithms. I.E.E.E. Trans. Autom. Control, Vol. AC. 28 no 3 (1983), pp.907–920.

    Article  MathSciNet  MATH  Google Scholar 

  4. O.P. Deveritskii, A.L. Fradkov, Two models for analysing the dynamics of adaptation algorithms. Automatika. I. Telemekhanika, no 1 (1974), pp.66–75.

    Google Scholar 

  5. E. Eweda, O. Macchi, Convergence analysis of an adaptive linear estimation algorithm. I.E.E.E. Trans. Autom. Control, Vol. AC. 29 no 2 (1984), pp.119–123.

    Article  MathSciNet  MATH  Google Scholar 

  6. E. Eweda, O. Macchi, Convergence analysis of self adaptive equalizers. I.E.E.E. Trans. Inf. Theory, Vol. IT-30 no 2 (1984), pp.161–176.

    MathSciNet  MATH  Google Scholar 

  7. V. Fabian, Stochastic approximation. In optimizing methods in statistics (Editor: J.S. Rustagi). Acad. Press, 1971, pp.439–470.

    Google Scholar 

  8. E.G. Gladyshev, On stochastic approximation. Theory of Probability and its applications. Vol. 10 (1985), pp.275–278.

    Article  Google Scholar 

  9. C.C. Heyde, D. Hall, Martingale limit theory and its applications. Acad. Press, 1980.

    Google Scholar 

  10. J. Kiefer, J. Wolfowitz, Stochastic estimation of the modulus of a regression function. Ann. Math. Stat. Vol. 23 (1952), pp. 462–466.

    Article  MathSciNet  MATH  Google Scholar 

  11. H. Kushner, Approximation and weak convergence methods for random processes, M.I.T. Press. Cambridge, 1984.

    MATH  Google Scholar 

  12. H. Kushner, D.S. Clark, Stochastic approximation methods for constrained and unconstrained systems.

    Google Scholar 

  13. H. Kushner, Stochastic approximation with discontinuous dynamics and state dependent noise. J. of Math. An. and Appl. Vol. 82 (1981), pp. 527–542.

    Article  MathSciNet  MATH  Google Scholar 

  14. H. Kushner, A. Shwartz, An invariant measure approach to the convergence of stochastic approximations with state dependent noise. S.I.A.M. 5. Control. Opt. Vol. 22 no 1 (1984).

    Google Scholar 

  15. L. Ljung, Analysis of recursive stochastic algorithms. I.E.E.E. Trans. Autom. Control. Vol. AC. 22 no 2 (1977), pp.551–575.

    Article  MathSciNet  MATH  Google Scholar 

  16. L. Ljung, T. Söderström, Theory and practice of recursive identification. M.I.T. Press, 1983.

    Google Scholar 

  17. M. Métivier, P. Priouret, Application of a Kushner and Clark. — Lemma to general classes of stochastic algorithms. I.E.E.E. Trans. Inf. Theory. IT-30 (1984), pp. 140–150.

    Article  MATH  Google Scholar 

  18. M. Métivier, P. Priouret, Théorèmes de convergence presque sure pour une classe d'algorithmes stochastiques. Preprint, Ecole Polytechnique, Palaiseau, (1984).

    MATH  Google Scholar 

  19. M. Métivier, P. Priouret, Convergence avec probabilité (1-ɛ) d'algorithmes stochastiques. Application au cas de l'egaliseur aveugle. To appear in Proceedings of the "Seminaire Quantification et Adaptativité". Nice Mai 85, Annales des Télécommunications.

    Google Scholar 

  20. M. Métivier, Introduction to stochastic approximation and adaptive filtering. Lecture Notes. Dipartimento di Matematica, Universita di Rome.

    Google Scholar 

  21. M. Métivier, Semimartingales. De Gruyter-Berlin, 1983.

    Google Scholar 

  22. M.B. Nevelson, R.Z. Has'Minski, Stochastic approximation and recursive estimation. A.M.S. Translations, Vol. 42.

    Google Scholar 

  23. H. Robbins, S. Monro, A stochastic approximation method. Ann. Math. Stat. Vol. 22 (1951), pp.400–407.

    Article  MathSciNet  MATH  Google Scholar 

  24. D. Ruppert, Almost sure approximation to the Robbins-Monro and Kiefer-Wolfowitz processes with dependent noise. The Ann. of Prob. Vol. 10 no 1 (1982), pp. 178–187.

    Article  MathSciNet  MATH  Google Scholar 

  25. D. Ruppert, Convergence of stochastic approximation algorithms with non additive dependent disturbances and applications. Preprint (1983).

    Google Scholar 

  26. M.T. Wasan, Stochastic approximation. Cambridge University Press (1968).

    Google Scholar 

  27. M.I. Freidlin, Random perturbations of dynamical systems. Springer, 1984.

    Google Scholar 

Download references

Author information

Authors and Affiliations

  1. Ecole Polytechnique, Palaiseau, France

    Michel Métivier

Authors
  1. Michel Métivier
    View author publications

    You can also search for this author in PubMed Google Scholar

Editor information

Kiyosi Itô Takeyuki Hida

Rights and permissions

Reprints and permissions

Copyright information

© 1986 Springer-Verlag

About this paper

Cite this paper

Métivier, M. (1986). On stochastic algorithms in adaptive filtering. In: Itô, K., Hida, T. (eds) Stochastic Processes and Their Applications. Lecture Notes in Mathematics, vol 1203. Springer, Berlin, Heidelberg. https://doi.org/10.1007/BFb0076879

Download citation

  • DOI: https://doi.org/10.1007/BFb0076879

  • Published:

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-16773-0

  • Online ISBN: 978-3-540-39852-3

  • eBook Packages: Springer Book Archive

Publish with us

Policies and ethics

Search

Navigation