Strong Limit Theorems Of Random Variables

The concep of NA was introduced by Joag-Dev and Proschan.Random variables, X₁, X₂,..., X_k, (k≥2)are said to be negatively associated(NA)if for every pair of disjoint subsets A₁, A₂of{1,...,k}, Cov[f(X_i, i∈A₁),g(X_j,j∈A₂)]≤0,for all nondecreasing function f, g. The basic property that nondecreasing function aremutually exclusive subsets of NA random Variables are NA. This property is shownnot to hold for other types of negative dependence recently proposed.Random variables, X₁, X₂,..., X_n (n≥2)are said to be associated, if for all non-decreasing function f, g. Cov[f(X_i, i∈A₁),g(X_j,j∈A₂)]≥0In Chanpter 2 of this thesis, we mainly discussed the Strong limit theores ofWeigth Sums for NA sequences with different distributions.This is the main part ofthis paper. In this chapter, under the《Strong limits theorems of weighted sumsfor NA sequences with distributions and its application in linear models》writen by Su Chun and Wang Yuebao, we weakened and improved the conditionsof the theores, proposed our own view and obtained the same conclusions Also, weproved the theorems minutely.And in Chanpter 3, we mainly discussed the Strong limit theorems of arbitraryrandom variables under moment conditions. Under the《Truncations of randomvariables and generalization of some classical strong laws of large nunmbers》writen by Yuan Demei,we creationed series new conditions and obtained the sameconclusions.