Geodesic
Conditions for the local convergence of recursive stochastic procedures
Teoriâ veroâtnostej i ee primeneniâ, Tome 28 (1983) no. 1, pp. 135-142 
V. V. Godovančuk; A. P. Korostelev. Conditions for the local convergence of recursive stochastic procedures. Teoriâ veroâtnostej i ee primeneniâ, Tome 28 (1983) no. 1, pp. 135-142. http://geodesic.mathdoc.fr/item/TVP_1983_28_1_a8/
@article{TVP_1983_28_1_a8,
     author = {V. V. Godovan\v{c}uk and A. P. Korostelev},
     title = {Conditions for the local convergence of recursive stochastic procedures},
     journal = {Teori\^a vero\^atnostej i ee primeneni\^a},
     pages = {135--142},
     year = {1983},
     volume = {28},
     number = {1},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/TVP_1983_28_1_a8/}
}
TY  - JOUR
AU  - V. V. Godovančuk
AU  - A. P. Korostelev
TI  - Conditions for the local convergence of recursive stochastic procedures
JO  - Teoriâ veroâtnostej i ee primeneniâ
PY  - 1983
SP  - 135
EP  - 142
VL  - 28
IS  - 1
UR  - http://geodesic.mathdoc.fr/item/TVP_1983_28_1_a8/
LA  - ru
ID  - TVP_1983_28_1_a8
ER  - 
%0 Journal Article
%A V. V. Godovančuk
%A A. P. Korostelev
%T Conditions for the local convergence of recursive stochastic procedures
%J Teoriâ veroâtnostej i ee primeneniâ
%D 1983
%P 135-142
%V 28
%N 1
%U http://geodesic.mathdoc.fr/item/TVP_1983_28_1_a8/
%G ru
%F TVP_1983_28_1_a8

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

We obtain the necessary and sufficient conditions for the almost sure convergence of recursive procedure (2.1) to the equilibrium stable state of the vector field $b(x)$. It is assumed that the trajectories of this procedure return a. s. into any neighbourhood of the equilibrium state. The convergence under this assumption is called local. Local convergence is studied for the cases of power (theorem 3.1) and subexponential (theorems 4.1 and 4.2) tails of distributions of random perturbations $\xi(t)$.