Approximation Properties Of The Robbins-Monro Algorithm

In the present article, we mainly study that the limit properties of Robbins-Monro algorithm of stochastic approximation, which include convergence and convergence rate of R-M algorithm.In the first chapter, we introduce the background of the stochastic approximation and state some known results. In addition, we propose our research directions and questions.In the second chapter, we study the extreme problems and establish some limit the-orem. There results improve achievements of original text, from tow ways. On the one hand, our article is weaker than Xu and Dai ([19]) whose propose that the conditions sat-isfy almost sure convergence. On the other hand, it is that we improve the results from mean square convergence to almost sure convergence which conditions are the same with original text.In the third chapter, we mainly proof the rate of convergence of the Robbins-Monro method which improves the related results of Komlos and Revesz ([10]).