On convergence of stochastic approximation procedures with dependent noise

The behavior of stochastic approximation procedures is studied in the case when the noise in the observations of an optimizing function derviative is a sequence of dependent random values. Sufficient conditions are defined for convergence almost surely and mean convergence of the order $p\geqslant2$. The proofs stem from results on convergence of dependent sequences which follow from theorems on convergence of mertigales.