Complete Convergence And Complete Moment Convergence For Widely Orthant Dependent Random Variables

At present,the research results of independent random variables in the theory of probability limit are relatively perfect,but the samples or variables are not necessarily independent in reality that so many scholars have pro-posed a dependent structure,such as negative associative variables(NA,in short),negative orthant dependent variable(NOD,in short),extended nega-tive orthant dependent variable(END,in short)and wide orthant dependent variable(WOD,in short),one of the most widely dependent variables is the WOD variable.At present,some scholars have a strong interest in it and get some meaningful results.Hence,it is significant and valuable to further study the WOD variable.In this paper,we firstly establish the complete convergence for weighted sums of WOD random variables and the maximum sequence of the weighted sums of WOD random variables by using the Rosential type maximal in-equality and the truncation technique of random variable under the general conditions,and give numerical simulation to verify its theoretical results are indeed effective.The complete moment convergence is a kind of convergence which is stronger than the complete convergence.Based on the complete con-vergence,we further study the complete moment convergence for weighted sums of WOD random variables.The results of this paper extend the corre-sponding results of some dependent variables.The complete convergence and the complete moment convergence of the WOD variables enrich and improve the probability limit theory of the WOD variable.