On martingale limit theory and strong convergence results for stochastic approximation procedures

AbstractThe analysis of asymptotic behaviour of stochastic approximation procedures rests heavily on the use of martingale limit theory, although explicit recognition of this situation is notable for its absence in the literature. This point is emphasized and in illustration a martingale iterated logarithm result is used to obtain strong convergence results of iterated logarithm type for the basic Robbins–Monro and Kiefer–Wolfowitz procedures