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Convergence of a general stochastic approximation process under convex constraints and some applications. (English) Zbl 0546.62057
Mathematical learning models - theory and algorithms, Proc. Conf., Bad Honnef/Ger. 1982, Lect. Notes Stat. 20, 156-167 (1983).
[For the entire collection see Zbl 0517.00013.]
A general stochastic approximation process (s.a.p.) in a closed convex subset of a separable Hilbert space is considered and a.s. convergence is proved. The results include as special cases the D. Ruppert’s dynamic s.a.p. [Ann. Stat. 7, 1179-1195 (1979; Zbl 0427.62059)], L. Ljung’s s.a.p. with correlated observations [ibid. 6, 680-696 (1978; Zbl 0402.62060)], as well as A. E. Albert and L. E. Gardner’s s.a.p.’s for estimating regression models [Stochastic approximation and nonlinear regression. (1967; Zbl 0162.215)]. The presentation is rather short, details being given in the author’s Ph. D. dissertation, Universit√© de Nancy I (1982).
Reviewer: R.Zielinski
MSC:
62L20 Stochastic approximation
62J02 General nonlinear regression
60F15 Strong limit theorems