A stochastic approximation procedure in the case of weakly dependent observations

The Robbins–Monro process is discussed. It is assumed that the observations, statistically dependent, satisfy Kolmogorov's mixing condition (1.7) or, for a special process $G$ (see condition (1.5)), Rosenblatt's mixing condition (1.6). The convergence of the Robbins–Monro process, its asymptotic normality and the convergence of moments are investigated.