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September, 1974 Some Generalizations of Dynamic Stochastic Approximation Processes
Katsuji Uosaki
Ann. Statist. 2(5): 1042-1048 (September, 1974). DOI: 10.1214/aos/1176342825


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.


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Katsuji Uosaki. "Some Generalizations of Dynamic Stochastic Approximation Processes." Ann. Statist. 2 (5) 1042 - 1048, September, 1974.


Published: September, 1974
First available in Project Euclid: 12 April 2007

zbMATH: 0288.62038
MathSciNet: MR359214
Digital Object Identifier: 10.1214/aos/1176342825

Primary: 62L20
Secondary: 93E20

Keywords: convergence in the mean square , convergence with probability one , maximum searching , root searching , sequential estimation , stochastic approximation

Rights: Copyright © 1974 Institute of Mathematical Statistics


Vol.2 • No. 5 • September, 1974
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