ABSTRACT
We consider a stochastic approximation procedure, present briefly its convergence properties, and sketch the proof of them. It is shown that the procedure converges if the sequence of weighted averages of certain random vectors almost surely converges to zero. The weights in those averages are related to the sequence of the amplification coefficients characterizing the procedure. Moreover, it is shown that the rapidness of the convergence of the procedure depends also on the rapidness of the convergence of the sequence of the amplification coefficients.
Sections 2 and 3 are devoted to the characterization of the set of all amplification coefficients for which convergence of the procedure takes place.
As by-products, we get theorems concerning generalized strong laws of large numbers for correlated random variables, with conditions for appropriate convergence expressed in terms 224of covariances. By generalized strong laws of large numbers we mean theorems concerning convergence to zero by weighted means rather than arithmetic means.
