Almost Sure Convergence For Weighted Sums Of A Class Of Random Variables

In this paper,we mainly prove the almost sure convergence of the weighted sums of a class of random variables,that is to say,for a class of random variables {Xn,n?1}and upper trigonometric constant matrix {an,k,1?k?n,n? 1}.In this paper,we are going to use a nondecreasing sequence of positive constants {cn} for cutting the random variables,proving them all apart.This article mainly includes the following items:1.The researching background of the weighted sums of random variables almost sure converges and the research status and achievements at home and abroad,the definition theorems and other preparatory knowledges needed to understand for completing this article;2.Almost sure convergence for weighted sums of a series of random variables {Xn,n?1} in and off cutting {cn};3.The application of the conclusion we get.In this paper,we do not study a certain random variable,but the weighted sums of a class of random variables converges almost sure and generalizing the conclusion above.