Abstract
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 language | English |
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Pages (from-to) | 133-149 |
Number of pages | 17 |
Journal | Stochastic Processes and their Applications |
Volume | 31 |
Issue number | 1 |
DOIs | |
State | Published - 1 Jan 1989 |
Keywords
- linear algorithms
- stochastic approximation in Banach space
- strong convergence
ASJC Scopus subject areas
- Statistics and Probability
- Modeling and Simulation
- Applied Mathematics