The Study Of Convergence For Weighted Sums Of (?,?) Mixing Sequence

The limit theory of dependent sequences is one of the central issues for studying probablity,which has very wide application in fields such as multivari-ate analysis,economic decisions and insurance actuarial science,reliability,weather forecast,survival analysis,engineering and technology and so on.In this arti-cle,we investigate convergence properties for weighted sums of negatively or-thant dependent random variables by several techniques such as inequality for moments,the truncated method for random variables,etc.,and obtain several mew results,our results improve and generalize the corresponding results of the cited references.Firstly,based on the moment inequality and maximal inequality for weighted suns of(?,?)mixing sequence,we obtain Marcinkiewicz-Zygmund-type strong law of large munbers for weighted suns of(?,?)mixing sequence.As a result,improving the corresponding results in Bai and Cheng,namely from indepen-dent and identically distributed random variables to(a,0)mixing sequence without adding any other conditions.Besides,by the truncated method,we also obtain strong convergence for Jamison-type weighted sums of(?,?)mixing sequence,which generalize the corresponding results in Wang.Secondly,with techniques of maximal inequality and truncated method,we pay much attention to complete convergence of weighted sums for arrays of rowwise(?,?)mixing sequence.Our results not only generalize the case of independent and identically distributed random variables in Baum and Katz,but also establish Marcinkiewicz-Zygmund-type strong law of large munbers for weighted sums of(?,?)mixing sequence.Finally,we study the complete moment convergence for double-indexed weighted sums of arrays of rowwise(?,?)mixing sequence.It generalizes the case for weighted sums of(?,?)mixing sequence,and it reveals the relationship of complete convergence in the complete moment converging process.Meanwhile,Marcinkiewicz-Zygmund-type strong law of large numbers for weighted sums of(?,?)mix-ing sequence has also been established,which generalizes the corresponding results of independent and identically distributed random variables and NA random variables.