Stochastic approximation with exciting perturbation under dependent noises

A stochastic approximation problem is considered in the situation when the unknown regression function is measured not at the previous estimate but at its slightly excited position. Errors of measurement are allowed to be either nonrandom or random with an arbitrary kind of dependence, and the zero-mean conditions are not imposed. Two estimation algorithms for estimating the root and the minimum point of regression function with projection is proposed. It is shown that the sequence of estimates {r_n} obtained converges to the true value θ as sure and in the mean square sense. Sequence of estimates has asymptotic normality distribution when we can propose some more about errors of measurement