Abstract stochastic approximations and applications

Adam Shwartz, Nadav Berman

Research output: Contribution to journalArticlepeer-review

8 Scopus citations


Results on the convergence with probability one of stochastic approximation algorithms of the form θn+1 = θn - γn+1 h(θn) + un+1 are given, where the θ'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 Kn+1 = Kn - 1 nXn{ring operator}[KnXn - Yn]. 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].

Original languageEnglish
Pages (from-to)133-149
Number of pages17
JournalStochastic Processes and their Applications
Issue number1
StatePublished - 1 Jan 1989


  • linear algorithms
  • stochastic approximation in Banach space
  • strong convergence

ASJC Scopus subject areas

  • Statistics and Probability
  • Modeling and Simulation
  • Applied Mathematics


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