Le processus d'approximation stochastique de Robbins-Monro : résultats théoriques ; estimation séquentielle d'une espérance conditionnelle

J. M. Monnez

Statistique et analyse des données (1979)

  • Volume: 4, Issue: 2, page 11-29
  • ISSN: 0750-7364

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Monnez, J. M.. "Le processus d'approximation stochastique de Robbins-Monro : résultats théoriques ; estimation séquentielle d'une espérance conditionnelle." Statistique et analyse des données 4.2 (1979): 11-29. <http://eudml.org/doc/108842>.

@article{Monnez1979,
author = {Monnez, J. M.},
journal = {Statistique et analyse des données},
language = {fre},
number = {2},
pages = {11-29},
publisher = {Association pour la statistique et ses illustrations},
title = {Le processus d'approximation stochastique de Robbins-Monro : résultats théoriques ; estimation séquentielle d'une espérance conditionnelle},
url = {http://eudml.org/doc/108842},
volume = {4},
year = {1979},
}

TY - JOUR
AU - Monnez, J. M.
TI - Le processus d'approximation stochastique de Robbins-Monro : résultats théoriques ; estimation séquentielle d'une espérance conditionnelle
JO - Statistique et analyse des données
PY - 1979
PB - Association pour la statistique et ses illustrations
VL - 4
IS - 2
SP - 11
EP - 29
LA - fre
UR - http://eudml.org/doc/108842
ER -

References

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  4. 4 - P. DAUBEZEUne extension d'un théorème de C. MACCHI. Annales Scientifiques de l'Université de Clermont, 1975, Mathématiques, 12ème fascicule, 64-93. Zbl0325.62053
  5. 5 - V. FABIANOn asymptotic normality in stochastic approximation. Ann. Math. Stat., 1968, Vol. 39, 1327-1332. Zbl0176.48402MR231429
  6. 6 - B. FICHETSur l'approximation et l'optimisation stochastiques. Thèse de docteur-ingénieur, Université Paul Sabatier de Toulouse, 1970. 
  7. 7 - E.G. GLADYSHEVOn stochastic approximation. Theory of Probability and its applications, 1965, Vol. 10, 275-278. 
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  9. 9 - R.L. KASHYAP, C.C. BLAYDON, K.S. FUStochastic approximation. Adaptive, learning and pattern recognition systems ; theory and applications, edited by J.M. Mendel, K.S. Fu, Academic Press, 1970, 329-355. Zbl0278.68083MR260084
  10. 10 - J. KIEFER, J. WOLFOWITZStochastic estimation of the maximum of a regression function. Ann. Math. Stat., 1952, Vol. 23, 462-466. Zbl0049.36601MR50243
  11. 11 - H.J. KUSHNERGeneral convergence results for stochastic approximations via weak convergence theory. Journ. Math. Anal, and applic., 1977, 61, 490-503. Zbl0369.62097MR458759
  12. 12 - H.J. KUSHNERConvergence of recursive adaptive and identification procedures via weak convergence theory. IEEE Trans. Autom. Contr., dec. 1977, Vol. AC-22, N° 6, 921-930. Zbl0389.93054MR484676
  13. 13 - L. LJUNGAnalysis of recursive stochastic algorithms. IEEE Trans. Autom. Contr., aug. 1977, Vol. AC-22, N° 4, 551-575. Zbl0362.93031MR465458
  14. 14 - L. LJUNGStrong convergence of a stochastic approximation algorithm. Ann. Stat., 1978, Vol. 6, N° 3, 680-696. Zbl0402.62060MR464516
  15. 15 - J.M. MONNEZApproximation stochastique : le processus de Robbins-Monro ; mise à jour des résultats et quelques compléments. Thèse de 3ème cycle, Université de Nancy I, 1975. 
  16. 16 - H. ROBBINS, S. MONROA stochastic approximation method. Ann. Math. Stat., 1951, Vol. 22, 400-407. Zbl0054.05901MR42668
  17. 17 - H. ROBBINS, D. SIEGMUNDA convergence theorem for non-negative almost supermartingales and some applications. Optimizing methods in Statistics, J.S. Rustagi ed., Academic Press, 1971, 233-257. Zbl0286.60025MR343355
  18. 18 - L. SCHMETTERERMultidimensional stochastic approximation. Multivariate Analysis, II, Proc. 2nd Int. Symp., Dayton, Ohio, Academic Press, 1969, 443-460. Zbl0104.12403MR258197
  19. 19 - J.H. VENTEROn Dvoretzky stochastic approximation theorems. Ann. Math. Stat., 1966, Vol. 37, 1534-1544. Zbl0146.39505MR203786

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