On stochastic approximation

Václav Dupač

Kybernetika (1981)

  • Volume: 17, Issue: Suppl, page (1)-40
  • ISSN: 0023-5954

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Dupač, Václav. "O stochastické aproximaci." Kybernetika 17.Suppl (1981): (1)-40. <http://eudml.org/doc/27409>.

@article{Dupač1981,
author = {Dupač, Václav},
journal = {Kybernetika},
keywords = {asymptotic normality; law of iterated logarithm; adaptive methods; robustness; review paper; Robbins-Monro procedure; martingale methods; Kiefer-Wolfowitz approximation},
language = {cze},
number = {Suppl},
pages = {(1)-40},
publisher = {Institute of Information Theory and Automation AS CR},
title = {O stochastické aproximaci},
url = {http://eudml.org/doc/27409},
volume = {17},
year = {1981},
}

TY - JOUR
AU - Dupač, Václav
TI - O stochastické aproximaci
JO - Kybernetika
PY - 1981
PB - Institute of Information Theory and Automation AS CR
VL - 17
IS - Suppl
SP - (1)
EP - 40
LA - cze
KW - asymptotic normality; law of iterated logarithm; adaptive methods; robustness; review paper; Robbins-Monro procedure; martingale methods; Kiefer-Wolfowitz approximation
UR - http://eudml.org/doc/27409
ER -

References

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  1. D. Anbar, On optimal estimation methods using stochastic approximation procedures, Ann. Statist. 1 (1973), 1175-1184. (1973) Zbl0277.62064MR0351001
  2. D. L. Burkholder, On class of stochastic approximation procedures, Ann. Math. Statist. 27 (1956), 1044-1059. (1956) MR0085653
  3. J. L. Doob, Stochastic Processes, J. Wiley, New York 1953. (1953) Zbl0053.26802MR0058896
  4. V. Dupač, A dynamic stochastic approximation, Ann. Math. Statist. 36 (1965), 1695 - 1702. (1965) MR0193724
  5. V. Dupač, O Kiefer-Wolfowitzově aproximační metodě, Časopis Pěst. Matem. 82 (1957), 47-75. (1957) MR0089556
  6. V. Dupač, On the dynamic stochastic approximation, Banach Center Publications, vol. 6, 109-110. Warszawa 1980. (1980) 
  7. V. Dupač F. Král, Robbins-Monro procedure with both variables subject to experimental error, Ann. Math. Statist. 43 (1972), 1089-1095. (1972) MR0336935
  8. V. Fabian, On asymptotic normality in stochastic approximation, Ann. Math. Statist. 39 (1968), 1327-1332. (1968) Zbl0176.48402MR0231429
  9. V. Fabian, Stochastic approximation of minima with improved asymptotic speed, Ann. Math. Statist. 38 (1967), 191-200. (1967) Zbl0147.18003MR0207136
  10. B. Ф. Ганошкин T. П. Красулина, О законе повторного логарифма в процессах стохастической аппроксимации, Teop. вepoятн. и ee примен. 19 (1974), 879 - 886. (1974) Zbl1235.49003
  11. L. Györfi, Stochastic approximation from ergodic sample for linear regression, Z. Wahrscheinlich. Verw. Geb. 54 (1980), 47-55. (1980) MR0595479
  12. D. L. Hanson R. P. Russo, A new stochastic approximation procedure using quantile curves, Z. Wahrscheinlich. Verw. Geb. (v tisku). 
  13. K. L. Chung, On a stochastic approximation method, Ann. Math. Statist. 25 (1954), 463 - 483. (1954) Zbl0059.13203MR0064365
  14. J. Komlós P. Révész, A modification of the Robbins-Monro process, Stud. Sci. Math. Hung. 8 (1973), 329-340. (1973) MR0351004
  15. T. П. Красулина, Метод стохастической аппроксимации для определения найбольшего собственного числа математического ожидания случайных матриц, Aвтоматика и телемеханика 1970, 2, 50- 56. (1970) Zbl1170.92319
  16. H. J. Kushner D. S. Clark, Stochastic Approximation Methods for Constrained and Unconstrained Systems, Springer-Verlag, New York 1978. (1978) MR0499560
  17. H. J. Kushner E. Sanvicente, Penalty function methods for constrained stochastic approximation, J. Math. Anal. and Applications 46 (1974), 499-512. (1974) MR0343506
  18. T. L. Lai H. Robbins, Adaptive design and stochastic approximation, Ann. Statist. 7 (1979), 1196-1221. (1979) MR0550144
  19. L. Ljung, Analysis of recursive stochastic algorithms, IEEE Trans. Autom. Control AC-22 (1977), 551-575. (1977) Zbl0362.93031MR0465458
  20. P. Major P. Révész, A limit theorem for the Robbins-Monro approximation, Z. Wahrscheinlich. Verw. Geb. 27 (1973), 79-86. (1973) MR0359213
  21. P. Mandl, Elements of stochastic analysis, Kybernetika 14 (1978), příloha. (1978) Zbl0382.60002MR0506651
  22. M. Б. Hевельсон P. З. Хасьминский, Стохастическая аппроксимация и рекуррентное оценивание, Hayкa, Mocквa. 1972. (1972) Zbl1049.82501
  23. G. Pflug, Stetige stochastische Approximation, Metrika 26 (1979), 139-150. (1979) Zbl0418.62066MR0548412
  24. P. Révész, How to apply the method of stochastic approximation in the nonparametric estimation of a regression function, Math. Operationsforsch. Statist., Ser. Statistics 8 (1977), 119-126. (1977) MR0501557
  25. P. Révész, Robbins-Monro procedure in a Hilbert space and its application in the theory of learning processes I, Stud. Sci. Math. Hung. 5 (1973), 391-398. (1973) MR0373198
  26. H. Robbins S. Monro, A stochastic approximation method, Ann. Math. Statist. 22 (1951), 400-407. (1951) MR0042668
  27. H. Robbins D. Siegmund, A convergence theorem for non negative almost supermartin-gales and some applications, In: Optimizing Methods in Statistics (J. S. Rustagi, ed.). Academic Press, New York 1971, 233-257. (1971) MR0343355
  28. W. Stout, A martingale analogue of Kolmogorov's law of the iterated logarithm, Z. Wahrscheinlich. verw. Geb. 15 (1970), 279-290. (1970) Zbl0209.49004MR0293701
  29. J. H. Venter, An extension of the Robbins-Monro procedure, Ann. Math. Statist. 38 (1967), 181-190. (1967) Zbl0158.36901MR0205396

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