Abstract
This chapter presents a set of recursive stochastic algorithms and their analysis. Typically, a sequence of estimates is obtained by means of some recursive statistical procedure. The nth estimate is some function of the (n – 1)th estimate and of some new observational data, and the aim is to study convergence and other qualitative properties (convergence rate) of the algorithm. A methodology has been presented for the derivation of the asymptotic properties of recursive stochastic algorithms. It has been discussed how to use directly results dealing with stochastic approximation techniques, well-known inequalities, the Lyapunov approach, and the martingale theory. In general, the problem of determining whether a given stochastic algorithm will converge or not requires a great deal of ingenuity and resourcefulness. It has been made easier by presenting a methodology, the complete analysis of two recursive algorithms, and many direct applications of the standard inequalities, well-known lemmas, and theorems.
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