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

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

2011-05-26

arxiv.org/abs/1105.5231v1

Mathematics

Statistics Theory

25 pages, 1 figure

Scientific paper

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

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