Martingale models of stochastic approximation and their convergence

Procedures of stochastic approximation are studied from a general theory of stochastic processes point of view. The results on convergence are obtained by the uniform methods both in the case of discrete and of continuous time. The asymptotic analysis (a.s. convergence, asymptotic normality) of procedures is based on the Lyapunov stochastic method, and a study of the rate of convergence of algorithms of stochastic approximation is based on the law of iterated logarithm for martingales.