Some generalizations of Dupac's dynamic stochastic approximation have been worked out to the more general cases of time variation. Sufficient conditions for convergence in the mean square and with probability one are given in case of deterministic trend and convergence with a bound is proved for the random trend case, using the estimation scheme $x_{n+1} = g_n(x_n) + a_n(\alpha - y_{n+1}(g_n(x_n)))$. This estimation procedure seems to be of practical use to a variety of problems in estimation, prediction and control.
Publié le : 1974-09-14
Classification:
Sequential estimation,
stochastic approximation,
convergence with probability one,
convergence in the mean square,
root searching,
maximum searching,
62L20,
93E20
@article{1176342825,
author = {Uosaki, Katsuji},
title = {Some Generalizations of Dynamic Stochastic Approximation Processes},
journal = {Ann. Statist.},
volume = {2},
number = {1},
year = {1974},
pages = { 1042-1048},
language = {en},
url = {http://dml.mathdoc.fr/item/1176342825}
}
Uosaki, Katsuji. Some Generalizations of Dynamic Stochastic Approximation Processes. Ann. Statist., Tome 2 (1974) no. 1, pp. 1042-1048. http://gdmltest.u-ga.fr/item/1176342825/