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Abstract stochastic approximations and applications

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  • Shwartz, Adam
  • Berman, Nadav

Abstract

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].

Suggested Citation

  • Shwartz, Adam & Berman, Nadav, 1989. "Abstract stochastic approximations and applications," Stochastic Processes and their Applications, Elsevier, vol. 31(1), pages 133-149, March.
    • Handle: RePEc:eee:spapps:v:31:y:1989:i:1:p:133-149
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    Cited by:

    1. Chen, Xiaohong & White, Halbert, 1998. "Nonparametric Adaptive Learning with Feedback," Journal of Economic Theory, Elsevier, vol. 82(1), pages 190-222, September.
    2. Chen Xiaohong & White Halbert, 2002. "Asymptotic Properties of Some Projection-based Robbins-Monro Procedures in a Hilbert Space," Studies in Nonlinear Dynamics & Econometrics, De Gruyter, vol. 6(1), pages 1-55, April.
    3. Perkins, S. & Leslie, D.S., 2014. "Stochastic fictitious play with continuous action sets," Journal of Economic Theory, Elsevier, vol. 152(C), pages 179-213.

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