Le processus d'approximation stochastique de Robbins-Monro : résultats théoriques ; estimation séquentielle d'une espérance conditionnelle
Monnez, J. M.
Statistique et analyse des données, Tome 4 (1979), p. 11-29 / Harvested from Numdam
Publié le : 1979-01-01
@article{SAD_1979__4_2_11_0,
     author = {Monnez, J. M.},
     title = {Le processus d'approximation stochastique de Robbins-Monro : r\'esultats th\'eoriques ; estimation s\'equentielle d'une esp\'erance conditionnelle},
     journal = {Statistique et analyse des donn\'ees},
     volume = {4},
     year = {1979},
     pages = {11-29},
     language = {fr},
     url = {http://dml.mathdoc.fr/item/SAD_1979__4_2_11_0}
}
Monnez, J. M. Le processus d'approximation stochastique de Robbins-Monro : résultats théoriques ; estimation séquentielle d'une espérance conditionnelle. Statistique et analyse des données, Tome 4 (1979) pp. 11-29. http://gdmltest.u-ga.fr/item/SAD_1979__4_2_11_0/

1 - C.C. Blaydon, R.L. Kashyap, K.S. Fu Applications of the stochastic approximation methods. Adaptive, learning and pattern recognition systems ; theory and applications, edited by J.M. Mendel, K.S. Fu, Academic Press 1970, 357-392. | MR 258194

2 - J.R. Blum Multidimensional stochastic approximation methods. Ann. Math. Stat., 1954, Vol. 25, 737-744. | MR 65092 | Zbl 0056.38305

3 - D.L. Burkholder On a class of stochastic approximation processes. Ann. Math. Stat., 1956, Vol. 27, 1044-1059. | MR 85653 | Zbl 0075.13803

4 - P. Daubeze Une extension d'un théorème de C. MACCHI. Annales Scientifiques de l'Université de Clermont, 1975, Mathématiques, 12ème fascicule, 64-93. | Numdam | Zbl 0325.62053

5 -V. Fabian On asymptotic normality in stochastic approximation. Ann. Math. Stat., 1968, Vol. 39, 1327-1332. | MR 231429 | Zbl 0176.48402

6 - B. Fichet Sur l'approximation et l'optimisation stochastiques. Thèse de docteur-ingénieur, Université Paul Sabatier de Toulouse, 1970.

7 - E.G. Gladyshev On stochastic approximation. Theory of Probability and its applications, 1965, Vol. 10, 275-278.

8 - J.L. Hodges, E.L. Lehmann Two approximations to the Robbins-Monro process. Proceedings of the Third Berkeley Symposium on Mathematical Statistics and Probability, University of California Press, 1956, Vol. 1, 95-104. | MR 84915 | Zbl 0072.36501

9 - R.L. Kashyap, C.C. Blaydon, K.S. Fu Stochastic approximation. Adaptive, learning and pattern recognition systems ; theory and applications, edited by J.M. Mendel, K.S. Fu, Academic Press, 1970, 329-355. | MR 260084 | Zbl 0278.68083

10 - J. Kiefer, J. Wolfowitz Stochastic estimation of the maximum of a regression function. Ann. Math. Stat., 1952, Vol. 23, 462-466. | MR 50243 | Zbl 0049.36601

11 - H.J. Kushner General convergence results for stochastic approximations via weak convergence theory. Journ. Math. Anal, and applic., 1977, 61, 490-503. | MR 458759 | Zbl 0369.62097

12 - H.J. Kushner Convergence of recursive adaptive and identification procedures via weak convergence theory. IEEE Trans. Autom. Contr., dec. 1977, Vol. AC-22, N° 6, 921-930. | MR 484676 | Zbl 0389.93054

13 - L. Ljung Analysis of recursive stochastic algorithms. IEEE Trans. Autom. Contr., aug. 1977, Vol. AC-22, N° 4, 551-575. | MR 465458 | Zbl 0362.93031

14 - L. Ljung Strong convergence of a stochastic approximation algorithm. Ann. Stat., 1978, Vol. 6, N° 3, 680-696. | MR 464516 | Zbl 0402.62060

15 - J.M. Monnez Approximation stochastique : le processus de Robbins-Monro ; mise à jour des résultats et quelques compléments. Thèse de 3ème cycle, Université de Nancy I, 1975.

16 - H. Robbins, S. Monro A stochastic approximation method. Ann. Math. Stat., 1951, Vol. 22, 400-407. | MR 42668 | Zbl 0054.05901

17 - H. Robbins, D. Siegmund A convergence theorem for non-negative almost supermartingales and some applications. Optimizing methods in Statistics, J.S. Rustagi ed., Academic Press, 1971, 233-257. | MR 343355 | Zbl 0286.60025

18 - L. Schmetterer Multidimensional stochastic approximation. Multivariate Analysis, II, Proc. 2nd Int. Symp., Dayton, Ohio, Academic Press, 1969, 443-460. | MR 258197 | Zbl 0104.12403

19 - J.H. Venter On Dvoretzky stochastic approximation theorems. Ann. Math. Stat., 1966, Vol. 37, 1534-1544. | MR 203786 | Zbl 0146.39505