Convergence and rate of convergence in iterative stochastic processes. I. The general case

The paper is concerned with iterative stochastic algorithms used in peak climbing control, statistics, in solution of optimization problems, adaptation, learning and pattern recognition. In terms of Lyapunov functions general results on convergence in some probabilistic sense (in the mean, almost sureby, with a probability of $1-\delta$) are formulated. Estimates of the rate of convergence are obtained.