Estimation of the Minimum Point of an Unknown Function Observed in the Presence of Dependent Noise

Stochastic approximation algorithms with input disturbances are proposed. From noisy observations of an unknown function dependent on a parameter, these algorithms produce consistent estimators of the minimum point of the function for the mean parameter value. The convergence of the algorithm is proved assuming that the test disturbance injected in the estimation procedure is independent of the observation noise. As an example, we consider estimation of the mean parameter values of the moving-average process observed in the presence of dependent noise.