Pairwise Nqd Column Convergence Properties

Limit theory is one of the key branches of Probability theory, and also the important foundation of other branches and Statistics.In this paper, we mainly discuss the strong stability for Jamison type wighted sums and Jamison type wighted prodect sums of pairwise NQD sequences, and the strong stability and complete convergences for pairwise NQD seqiiences.It is divided into four chapters as follows:In the first chapter,we first give some concepts of the associated sequences including pairwise NQD sequences.then summarize some important results given by domestic and foreign scholars, and indicate their theoretical and practical value.In the second chapter,we first introduce the development of Jamison type wighted sums and Jamison type wighted prodect sums, then extend the results of independent identically distributed random variables sequences and NA sequences about Jamison type wighted sums to pairwise NQD sequences, and discuss the strong stability for Jamison type wighted prodect sums of pairwise NQD sequences.In the third chapter,we first give the concept of the strong stability and introduce some results of independent identically distributed random variables sequences and NA sequences,with the same condition we extend the results we had got and get the Marcinkiewicz strong law of large numbers for pairwise NQD sequences.In the forth chapter ,we discusse the complete convergence for pairwise NQD sequences,and get the Baum-Katz's theory on complete convergence for pairwise NQD sequences with different distribution.