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Abstract stochastic approximations and applications


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  • Shwartz, Adam
  • Berman, Nadav
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    Results on the convergence with probability one of stochastic approximation algorithms of the form [theta]n+1 = [theta]n - [gamma]n+1 h([theta]n) + un+1 are given, where the [theta]'s belong to some Banach space and {un} is a stochastic process. Using this extension of results of Kushner and Clark [10], conditions are given for the convergence of the linear algorithm . Several applications of the linear algorithm to problems of identification of (possibly distributed) systems and optimization are given. The applicability of these conditions is demonstrated via an example. The systems considered here are more general than those considered by Kushner and Shwartz [12].

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    Bibliographic Info

    Article provided by Elsevier in its journal Stochastic Processes and their Applications.

    Volume (Year): 31 (1989)
    Issue (Month): 1 (March)
    Pages: 133-149

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    Handle: RePEc:eee:spapps:v:31:y:1989:i:1:p:133-149

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    Keywords: stochastic approximation in Banach space strong convergence linear algorithms;


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    Cited by:
    1. Chen, Xiaohong & White, Halbert, 2002. "Asymptotic Properties of Some Projection-based Robbins-Monro Procedures in a Hilbert Space," University of California at San Diego, Economics Working Paper Series qt4z4380t7, Department of Economics, UC San Diego.
    2. Chen, Xiaohong & White, Halbert, 1998. "Nonparametric Adaptive Learning with Feedback," Journal of Economic Theory, Elsevier, vol. 82(1), pages 190-222, September.


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