Moving Average Process Under Dependent Sample Moment Complete Convergence

Complete convergence in probability theory limit theory is an important conceptof traditional, since Paul and Robbins introduced treasure complete convergenceconcepts.Much papers have discussed the independent and dependent random variablesseries complete convergence. This project in today’s international statistics in theworld of research is very active. It has certain application prospectin theory. This paper (especially in mixing, mixing, mixing) furtherdiscusses complete convergence of the process of moving average in the mixedsamples.This paper has four parts, the first chapter,we introduce the definition of completeconvergence and mixing sequence of definition, and several lemmas and proof of thetheorem. The sec o nd chapter presents the definition of mixing sequence, movingaverage processes, as well as several lemmas and proof of the theorem. The thirdchapter present s t he definition of mixing sequence, hold inequality and severallemmas and proof of the theorem.The fourth chapter,we introduce the definition ofcomplete convergence and NA mixing sequence of definition, and several lemmas andproof of the theorem.