The Precise Asymptotics Of Complete Moment Convergence For NA And ?-mixing Sequence

Limit theory of dependent sequences have vital application in a lot of fields such as finance and statistics,insurance,natural science,engineering,reliability analysis and other fields,therefore,one of the hot spots in the study of probability limit theory is that to study the series of dependent random variables by breaking through the constraints of independent conditions,to deepen the classical basic results of independent random variables and to expand the research field of random sequence.While the precise asymptotic theory is an important topic in the study of limit theory,it not only deepens the research of the complete moment convergence,but also has a great significance to improve the probability limit theory system.In this paper,we mainly study the precise asymptotic of NA sequences and ?-mixing sequence.Firstly,based on the research of Fu and Yang,we extend the logarithmic factor(?)logn of complete moment convergence into a more general form of(logn)d,and use the correlation properties of NA sequence and the method of precise asymptotic.As a result,we establish a general formula for the precise asymptotic of the complete moment convergence of NA sequences under logarithmic rate,which deepening the Fu and Yang results and expanding the scope of its application.Then,after research on the two order moment,logarithm and the law of the iterated logarithm,we obtain three kinds of expressions of precise asymptotic of complete moment convergence on moving average process for ?-mixing sequence by using the central limit theorem and moment inequality and its probability inequality based on moving average process of ?-mixing sequence and the method of multiple censoring,which not only generalize the corresponding conclusions,but also further improve the ?-mixing sequence limit theory.