The Studies Of Convergence Properties For The Partial Sums Of Pairwise NQD Sequence

Strong laws of large numbers are one of the main aims in the probability and limit theory. The classical theories on the strong laws of large numbers have been developed completely. In the recent years, many authors have studied the probability and limit theory about the dependent sequences and their important inequalities such as Rosenthal-type inequality, and so forth. These important inequalities about the dependent sequences, especially moment inequalities, provide an important tool to study the strong laws of large numbers. In this paper, based on the moment inequality of pairwise NQD sequence and the truncated method of random variables, the strong laws of large numbers are obtained. In addition, using the generalized three series theorem of pairwise NQD and the truncated method of random variables, the strong limit theorems and the strong laws of large numbers are obtained under some moment conditions. These results extend the ones of the independent sequence and the pairwise NQD sequence. The paper is organized as follows:Using the moment inequalities and the truncated methods of random variables, we get the strong laws of large numbers. The results extend the corresponding ones of independent and pairwise NQD sequence.In view of the truncated method of random variables and the generalized three series theorem, we discuss the properties of pairwise NQD and obtain a kind of the strong law of large numbers and strong limit theorems under moment conditions, which extend the corresponding results of classical strong laws of large numbers.