Strong Convergence Properties For ANA Random Variables

The limit theory of dependent sequences is one of the central issues for prob-ability,which has wide application in many fields such as economic decisions and insurance,weather forecast,multivariate statistical analysis,reliability and so on.In this article,we investigate convergence properties for ANA random variables by several techniques such as maximal inequality,Markov inequality,Cr inequality,Borel-Cantelli lemma and the truncated method for random variables,and so on.We obtain some new results for ANA random variables.The complete convergence and complete moment convergence for weighted sums of ANA random variables are obtained.We also give some strong law of large numbers for ANA random variables.ANA random variables include ρ-mixing and NA random variables.Li et al[9]studied complete convergence for weighted sums of ρ-mixing random variables.Chen and Sung[46]studied complete convergence for weighted sums of NA random variables.Firstly,we extend the results of Li et al[9]and Chen and Sung[46]to rowwise ANA random variables.The complete convergence for a sequence of mean zero ANA random variables are obtained.Secondly,when 1<α≤ 2,the com-plete moment convergence for weighted sums of rowwise ANA random variables are discussed.Finally,the strong law of large numbers for ANA random variables are obtained.The strong convergence properties for ANA random variables enrich and improve the probability limit theory of ANA random variables.