Behavior Of Pairwise Nqd Random Variables Weighted Sums Of Arrays Of Convergence

Limit theory is one of the key branches of Probability theory, and also it is the important foundation of other branches and Statistics. Convergence plays an important part in Probability Limit Theory. There are a series of convergence conceptions such as convergence in probability, convergence in distribution, almost sure convergence etc. In this paper, we mainly discuss several kinds of convergences for the weighted sums of pairwise NQD random arrays and sums of pairwise NQD random matrix sequence under the condition of h-integrability, and strong law of large numbers for the sum of partial sum of NQD random sequences. It is devided into five chapters as follows:In the first chapter, we first give some concepts of NQD sequences and some kinds of integrability, then summarize some important results given by domestic and foreign scholars, and indicate their theoretical and practical value.In the second chapter, we mainly discuss Lr convergence for the weighted sums of pairwise NQD random arrays. The early paper has discussed Lr convergence for pairwise NQD random sequences under r-means Cesaro uniform integrability. we discuss Lr convergence for the weighted sums of pairwise NQD random arrays under the condition of h-integrability which is weaker than Pingyan Chen's, and it extends the results before.In the third chapter, we mainly discuss the complete convergence for the weighted sums of pairwise NQD random arrays, under the condition of h-integrability. And it leads the results of J.I.Baek's to a special case. Also, we extend the results of Qunying Wu's.In the fourth chapter, we discuss the weak law of large numbers, Lr convergence and complete convergence of sums of pairwise NQD random matrix sequence, under the related condition of h-integrability. And we extend the results of Qunying Wu's.At last, we mainly discuss strong law of large numbers for the sum of partial sum of NQD sequences, references [25,26] have discussed strong law of large numbers for the sum of partial sum of I.I.D sequences. In this paper, we do some research on strong law of large numbers for the sum of partial sum of pairwise NQD sequences convergence, and also it extends the results before.