Geodesic
A~criterion for convergence of continuous stochastic approximation procedures
Teoriâ veroâtnostej i ee primeneniâ, Tome 22 (1977) no. 3, pp. 595-602

Voir la notice de l'article provenant de la source Math-Net.Ru

For the a.s. convergence of the stochastic approximation procedure $$ dX_s=\alpha(s)[\triangledown f(X_s)+\varphi(s,X_s)]\,ds+\beta(s)\sigma(s,X_s)\,dW_s $$ to a maximum point of $f$, the following condition is proved to be necessary and sufficient: for any $\lambda>0$ $$ \int_0^{\infty}\exp(-\lambda\gamma^{-2}(t))\,dt\infty $$ where $dt=\alpha(s)\,ds$; $\gamma(t)=\beta(t)/\sqrt{\alpha(t)}$. 
@article{TVP_1977_22_3_a14,
     author = {A. P. Korostelev},
     title = {A~criterion for convergence of continuous stochastic approximation procedures},
     journal = {Teori\^a vero\^atnostej i ee primeneni\^a},
     pages = {595--602},
     publisher = {mathdoc},
     volume = {22},
     number = {3},
     year = {1977},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/TVP_1977_22_3_a14/}
}
TY  - JOUR
AU  - A. P. Korostelev
TI  - A~criterion for convergence of continuous stochastic approximation procedures
JO  - Teoriâ veroâtnostej i ee primeneniâ
PY  - 1977
SP  - 595
EP  - 602
VL  - 22
IS  - 3
PB  - mathdoc
UR  - http://geodesic.mathdoc.fr/item/TVP_1977_22_3_a14/
LA  - ru
ID  - TVP_1977_22_3_a14
ER  - 
%0 Journal Article
%A A. P. Korostelev
%T A~criterion for convergence of continuous stochastic approximation procedures
%J Teoriâ veroâtnostej i ee primeneniâ
%D 1977
%P 595-602
%V 22
%N 3
%I mathdoc
%U http://geodesic.mathdoc.fr/item/TVP_1977_22_3_a14/
%G ru
%F TVP_1977_22_3_a14
A. P. Korostelev. A~criterion for convergence of continuous stochastic approximation procedures. Teoriâ veroâtnostej i ee primeneniâ, Tome 22 (1977) no. 3, pp. 595-602. http://geodesic.mathdoc.fr/item/TVP_1977_22_3_a14/