Convergence of recursive adaptive and identification procedures via weak convergence theory

Abstract

Results and concepts in the theory of weak convergence of a sequence of probability measures are applied to convergence problems for a variety of recursive adaptive (stochastic approximation-like) methods. Similar techniques have had wide applicability in areas of operations research and in some other areas in stochastic control. It is quite likely that they will play a much more important role in control theory than they do at present, since they allow relatively simple and natural proofs for many types of convergence and approximation problems. Part of the aim of the paper is tutorial: to introduce the ideas and to show how they might be applied. Also, many of the results are new, and they can all be generalized in many directions.