Dependent Random Variable Sequence Part And The Convergence Rate

Probability Limit Theory is one of the important braches and essential theoretical foundations of science of Probability and Statistics.A research direction of modern Probability Limit Theory is to weaken the restrictions of "independence" so as to be closer to reality and to make for application. In this paper, we study the convergence rate of partial sum of some dependent random variable sequences and obtain some results which extend and improve the corresponding known ones.In preface, we introduce some kinds of dependent random variable sequences, definition of some convergences and relations between of them as well as recent research headway of pairwise NQD sequences. We also introduce notion of precise asymptotics and recent research headway of precise asymptotics in brief.In chapter one, we discuss the Lr convergence for pairwise NQD random variable sequences of domains of attraction of a stable distribution. Qi and Cheng have obtained Laws of Iterated Logarithm for partial sum of i.i.d. random variable of domains of attraction of a stable distribution. Lai has obtained limit property for weighted sums ofφ-mixing sequences of random variables of domains of attraction of a stable distribution.In this chapter, A result on Lr Convergence for pairwise NQD random variable sequences of domains of attraction of a stable distribution under common conditions is given, which is the same as that in the independent case.In chapter two, we discuss the complete convergence of moving average processes for non-indentically pairwise NQD random variable sequences.Complete convergence property is an important convergence property of sequences of random variables. There are lots of perfect results of independent sequences of random variables. Cai research into the complete convergence of moving average processes for NA random variable sequences; Wang,et al study the complete convergence of moving average processes for LNQD random variable sequences. In this chapter, we obtain a result on the complete convergence of moving average processes for non-indentically pairwise NQD sequences, which is the same as that in the independent case.In chapter three, we discuss the precise asymptotics in the Baum-Katz and Davis law of large numbers for LNQD random variable sequences. In this chapter, we obtain some results on the precise asymptotics in the Baum-Katz and Davis laws of large number for LNQD sequences under certain condition, which is similar to corresponding known ones.