On Bather's stochastic approximation algorithm
Kybernetika, Tome 30 (1994) no. 3, pp. 301-306 Cet article a éte moissonné depuis la source Czech Digital Mathematics Library

Voir la notice de l'article

Classification : 62L20
@article{KYB_1994_30_3_a9,
     author = {Schwabe, Rainer},
     title = {On {Bather's} stochastic approximation algorithm},
     journal = {Kybernetika},
     pages = {301--306},
     year = {1994},
     volume = {30},
     number = {3},
     mrnumber = {1291932},
     zbl = {0810.62077},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/KYB_1994_30_3_a9/}
}
TY  - JOUR
AU  - Schwabe, Rainer
TI  - On Bather's stochastic approximation algorithm
JO  - Kybernetika
PY  - 1994
SP  - 301
EP  - 306
VL  - 30
IS  - 3
UR  - http://geodesic.mathdoc.fr/item/KYB_1994_30_3_a9/
LA  - en
ID  - KYB_1994_30_3_a9
ER  - 
%0 Journal Article
%A Schwabe, Rainer
%T On Bather's stochastic approximation algorithm
%J Kybernetika
%D 1994
%P 301-306
%V 30
%N 3
%U http://geodesic.mathdoc.fr/item/KYB_1994_30_3_a9/
%G en
%F KYB_1994_30_3_a9
Schwabe, Rainer. On Bather's stochastic approximation algorithm. Kybernetika, Tome 30 (1994) no. 3, pp. 301-306. http://geodesic.mathdoc.fr/item/KYB_1994_30_3_a9/

[1] J. A. Bather: Stochastic approximation: A generalisation of the Robbins-Monro procedure. In: Proc. Fourth Prague Symp. Asymptotic Statistics, Charles Univ. Prague, August 29-September 2, 1988 (P. Mandl and M. Hušková, eds.), Charles Univ., Prague 1989, pp. 13-27. | MR

[2] J. R. Blum: Approximation methods which converge with probability one. Ann. Math. Statist. 25 (1954), 382-386. | MR | Zbl

[3] K. L. Chung: On a stochastic approximation method. Ann. Math. Statist. 25 (1954), 463-483. | MR | Zbl

[4] V. Fabian: On asymptotic normality in stochastic approximation. Ann. Math. Statist. 39 (1968), 1327-1332. | MR | Zbl

[5] G. Kersting: Almost sure approximation of the Robbins-Monro process by sums of independent random variables. Ann. Probab. 5 (1977), 954-965. | MR | Zbl

[6] L. Ljung: Strong convergence of a stochastic approximation algorithm. Ann. Statist. 6 (1978), 680-696. | MR | Zbl

[7] B. T. Polyak: New method of stochastic approximation type. Automat. Remote Control 51 (1990), 937-946. | MR | Zbl

[8] H. Robbins, S. Monro: A stochastic approximation method. Ann. Math. Statist. 22 (1951), 400-407. | MR | Zbl

[9] D. Ruppert: Almost sure approximations to the Robbins-Monro and Kiefer-Wolfowitz processes with dependent noise. Ann. Probab. 10 (1982), 178-187. | MR | Zbl

[10] D. Ruppert: Efficient Estimators from a Slowly Convergent Robbins-Monro Process. Technical Report No. 781, School of Operations Research and Industrial Engineering, Cornell Univ. Ithaca 1988.

[11] D. Ruppert: Stochastic approximation. In: Handbook of Sequential Analysis. (B. K. Ghosh and P. K. Sen, eds.), Marcel Dekker, New York 1991, pp. 503-529. | MR

[12] J. Sacks: Asymptotic distribution of stochastic approximation procedures. Ann. Math. Statist. 29 (1958), 373-405. | MR | Zbl

[13] R. Schwabe: Strong representation of an adaptive stochastic approximation procedure. Stochastic Process. Appl. 23 (1986), 115-130. | MR | Zbl

[14] R. Schwabe: Stability results for smoothed stochastic approximation procedures. Z. Angew. Math. Mech. 73 (1993), 639-643. | MR | Zbl

[15] J. H. Venter: An extension of the Robbins-Monro procedure. Ann. Math. Statist. 38 (1967), 181-190. | MR | Zbl

[16] H. Walk: Foundations of stochastic approximation. In: Stochastic Approximation and Optimization of Random Systems, DMV Seminar Blauberen, May 28-June 4, 1989 (L. Jung, G. Pflug and H. Walk, eds.), DMV Seminar, Vol. 17, Birkhäuser, Basel 1992, pp. 1-51.