Approximationalgorithm Basedon Random Censored

Stochastic approximation is a mathematical statistics method to estimate a particular value through the successive approximation approach when it is under random error interference, and now it’s widely applied in the fields of electronic technology, application control and so on. Now a lot of articles are describing stochastic approximation, but only few are about the iteration truncation. Of Stochastic approximation algorithms the most classical one is "Accelerated Stochastic Approxi-mation Algorithm Based On the Arithmetic Average Method" which was written by Polayak B.T and Juditsky A.B in1992. This article, which demonstrates the strong consistency and asymptotic normality of random sequences in linear and nonlinear systems, has promoted the further development of stochastic approximation algorithm. However, in modern society, especially in the era of big data, the data itself are dirty, and need to be cleaned, or these noise data will greatly affect the complexity of our algorithm and the convergence speed, and cost us much time, so during the process of operation, cleaning data has become the necessary link. Similarly, the stochastic approximation algorithms such noise data will also appear in the process of iteration, and the common approach of smoothing data is using the truncation method, which is also the source of ideas for this article.This article investigates the stochastic approximation problem with stochastic disturbances linear systems and makes some modifications of the iterative algorithm in the linear part of "Accelerated Stochastic Approximation Algorithm Based on the Arithmetic Average Method" which was written by Polayak B.T and Juditsky A.B in1992. Truncating the iteration items, this article demonstrates that stochastic approximation sequence can successively converge to a random variable of normal distribution, and converge to zero almost everywhere. Our article also accelerates the convergence rate of algorithm and proves the strong consistency and asymptotic normality of random sequences under this algorithm.