On Complete Moment Convergence For Sequence Ofφ-mixing Random Variables

Probability limit theory is not only one of the main branches of proba-bility theory, but also is an important theoretical foundation of other fieldsof probability and statistics.In1930s and1940s, the classical limit theoremsof probability theory for independent random variables had been obtained amore comprehensive development.However, many samples in the world arenot independent.Therefore, the study of dependent random variables is morepractical significance.In this paper, we mainly discuss the complete moment convergence ofmoving average processes under-mixing random variables. It is divided into four chapters as follows:In chapter one, we first give some concepts of complete convergence and-mixing random variables. Then summarize some important results givenby domestic and foreign scholars, and indicate their theoretical and practicalvalue.In chapter two, We prove the complete moment convergence of movingaverage processes under some suitable conditions, improving the results ofZhang [14] and Kim et al.[11]. Moreover, our methods difer from those usedby Kim et al.(2008).In chapter three, we study the complete moment convergence of weightedsums for arrays of rowwise-mixing random variables. And obtain the com-plete moment convergence of moving average processes based on a-mixingrandom sequences, which extend and improve the result of Kim et al [11].