Teoriâ veroâtnostej i ee primeneniâ, Tome 22 (1977) no. 3, pp. 595-602
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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/
@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},
year = {1977},
volume = {22},
number = {3},
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
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
%U http://geodesic.mathdoc.fr/item/TVP_1977_22_3_a14/
%G ru
%F TVP_1977_22_3_a14
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 $dt=\alpha(s)\,ds$; $\gamma(t)=\beta(t)/\sqrt{\alpha(t)}$.
