The Complete Convergence And Central Limit Theorem Of Random Fields

The development of the concept of random fields is more and more widely used in modern society and has penetrated into every corner of science.Besides,the study of the central limit theorem and the moderate deviation principle has been very rich results,and the results have been widely used in mathematical statistics,financial insurance,economic life and information theory.In this paper,we mainly study the estimation of the moderate deviation principle,complete convergence and the convergence rate of central limit theorem related to random fields.Specifically,in chapter 1,we introduce the research background and significance of this paper.In chapter 2,we discusses the complete convergence of a simple linear random field and give the moderate deviation principle of random fields by using the Lindeberg method.In chapter 3,we mainly study the error estimation of the central limit theorem of random fields and get Berry-Esseen estimation.