Abstract
A stochastic approximation procedure is proposed for finding a point on a discrete set which gives the maximum of a function defined and observable only at points on the discrete set based on the noisy observations. Here, we call a discrete set as a set of points of integral multiples of some unit. It is proved by using the theorem of almost supermartingale that the estimate converges with probabilty one to the true maximum as the number of observation tends to infinity. A numerical example is presented for illustrating the convergence. The procedure can be applied to recursive identification of time serie model.
