The Convergence Of Weighted Sums Under Negative Dependence

Probability limit theory with unique way of thinking,hightly abctract,close logica,is the important branch of the theory of probability, and also is the important theoretical basis of probability and statitics.The clssical theory of probability limit theory is based on independent random variable.But in fact,most samples are independent,therefore dependent random variables is attented by scholars.Negative dependent is one type of dependent random variables.Since the weighe of random variables is different in probability samples, the weighted sums of negative dependent is a hot topic in rencent years.The concepet of negative dependent first prpposed by Joag-Dev and Proschan in 1983.then Newman,Matula,Kolmogorov,Petrov,Taylor,Zarei and Jabbari.What's more, there are also same chinese scholars such as Su Chun,Liu Xuguo,Lin Zhengyan,Chi Xiang,Qing Yongsong etc. are studied the weighted sums of negative dependent.In this paper,we use stochastic controls,consored,and some moment inequallities of negative associated random variables sum up negative associated random results in rencent 10years.and obtain severral conclusions of the weighted sums of negative associated random variables.Firstly, use stochastic controls extend the Hsu and Robbin, Zarei and Jabbari's theorem from the case of identically distributed random variables to dentically distributed random variables .Secondly,use stochastic control discuss negative array associated random variables obtain weighted sums of negative associated random variables application in linear time series.Finally, use stochastic controls analysia some strong convergence and extend the strong convergence theorem from the case of identically distributed random variables to dentically distributed negative associated random variables.