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It is shown the almost sure convergence and asymptotical normality of ageneralization of Kesten's stochastic approximation algorithm formultidimensional case. In this generalization, the step increases or decreasesif the scalar product of two subsequente increments of the estimates ispositive or negative. This rule is intended to accelerate the entrance in the`stochastic behaviour' when initial conditions cause the algorithm to behave ina `deterministic fashion' for the starting iterations.

Almost sure convergence and asymptotical normality of a generalization of Kesten's stochastic approximation algorithm for multidimensional case