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Convergence of methods for stochastic approximation in a Banach space. (English. Ukrainian original) Zbl 0838.62075

Theory Probab. Math. Stat. 48, 1-5 (1994); translation from Teor. Jmovirn. Mat. Stat. 48, 3-9 (1993).

Summary: Necessary and sufficient conditions are described for convergence with probability 1 of linear methods for stochastic approximation in a separable Banach space to the root of the corresponding operator equation.

Cited in 1 Document

MSC:

62L20	Stochastic approximation
60B12	Limit theorems for vector-valued random variables (infinite-dimensional case)
47N30	Applications of operator theory in probability theory and statistics

Keywords:

Robbins-Monro method; Gaussian perturbations; linear methods; separable Banach space; root

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