On Complete Moment Convergence Of Weighted Sums For Arrays Of Row-wise AANA Random Variables

In social activities,random event shows a certain regularity in some sense when repeats a lot.Men tried to study this regularity on random events in mathematical method,a new subject of probability theory set up consequently.Based on measure theory,modern probability theory-sprung up in the early 20th century and separated into different branches,such as limit theory、stochastic analysis and so on.However,limit theory is one of important research direction in probability theory and mathe-matical statistics which has abundant meaningful limit theorems based on the convergence of random variables.In this paper,complete convergence and complete moment convergence of random variables are studied in the main,especially AANA random variables.Due to the dependence of ran-dom variables in application of practical matters,Chandra and Ghosal(1996)give the concept of AANA(asymptotically almost negatively as-sociated),and what we get is the theorem of complete convergence and complete moment convergence of weighted sums for arrays of row-wise AANA random variables.In the first chapter,we show the research background of this paper and emphasize the concept of AANA,the definition of complete conver-gence as well as complete moment convergence.What’s more,the details of development of dependent random variables from concept to relative theorems will be introduced for the further study of readers.In the second chapter,by using truncation method and Rosenthal type inequality,the sufficient condition of complete convergence of weighted sums for arrays of row-wise AANA random variables is investigated,which generalize the result of Shen’s.We prove the theorem of Wang’s and the proof procedure is simplified greatly.In the third chapter,we mainly discuss the complete moment conver-gence of weighted sums for arrays of row-wise AANA random variables.First we improve the result of Guo’s[21]on complete moment convergence of weighted sums for arrays of row-wise NA random variables to the AANA random variables,and extend the corresponding results of Wang’s[28]from the complete convergence to the complete moment convergence.Next,we study some theorems of complete qth moment convergence of weighted sums for arrays of row-wise AANA random variables which complement the property of AANA random variables.