Exact bounds for the rate of convergence in general stochastic approximation procedures

Abstract

In this paper exact constants are given for the rate of convergence of the solution x _n of the nonlinear difference equation towards the root θ of f under very general conditions on the steplengths a_n , on the weighting factors b_n and on the random noise v_n . Moreover, an almost sure representation is developed for the deviation x_n – θ by weighted sums of (independent) random variables

^‡supported by the research grants Ku719/2-1 and Ku719/2-2 of the Deutsche Forschungsgemeinschaft

^‡supported by the research grants Ku719/2-1 and Ku719/2-2 of the Deutsche Forschungsgemeinschaft

Notes

^‡supported by the research grants Ku719/2-1 and Ku719/2-2 of the Deutsche Forschungsgemeinschaft