Precise Asymptotics Of Some Types Of Random Variable Sequences

The probability limit theory is the basic theory of the probability theory and mathematical statistics and other disciplines,and it has a very important position in the statistics.The precise asymptotics is an important research topic in the probability limit theory,and the concept of precise asymptotic theory has been put forward,which has greatly broadened the research scope of the probability limit theory.Currently,the classical precise asymptotics of independent sequence has been well developed.However,although in some case the independence assumption is reasonable,the sample is not possible to satisfy the independence in all practical problems.So the study of the precise asymptotics of dependent sequences is of great significance.This dissertation is based on the basic properties and some inequality of dependent sequence and use the method of limit theory,mainly from the following several aspects to research work:Firstly,we study the precise asymptotics of NA random variables.We use the central limit theorem and some probability inequalities for NA random variables and use some methods and means of precise asymptotics.The precise asymptotics in the law of iterated logarithm for the moment convergence of NA random variables are obtained.Then we generalize the corresponding results of independence sequence.Secondly,this dissertation study the precise asymptotics of ?-mixing random variables.By using the central limit theorem and the probability inequality and the moment inequality for ?-mixing ran-dom variables and combine the nature and characteristics of moving average processes,we obtained the precise asymptotics of complete moment convergence of ?-mixing moving average process and complete moment convergence rate of moving average processes for ?-mixed sequences.Then we generalize the corresponding results.Finally,this dissertation study the precise asymptotics of ?-mixing random variables.Using the mo-ment inequality and the central limit theorem of the ?-mixing random variables.The precise asymptotics in the law of iterated logarithm for the moment convergence of ?-mixing random variables of the partial sum and the maximum of the partial sum aer obtained.