Complete Convergence For Sequences Of Na Random Variables

In this thesis, we study the complete convergence for sequences of NA random variables. Thisthesis is divided into three chapters.In chapter 1, we give the overall introduction.In chapter 2, we consider the complete convergence for randomly weighted sums Sn = ni=1WiXiassociated to a negatively associated sequence {Xn,n≥1}, where {Wn,n≥1} is a randomsequence. By using probability inequalities of NA and the truncated method, under EXn2 <∞and the moment condition of random sequence {Wn,n≥1}, several su?cient conditions for thecomplete convergence of randomly weighted sums Sn are obtained.In chapter 3, we consider the complete convergence for weighted sums Sn = ni=1aniXi asso-ciated to a m-negatively associated sequence {Xn,n≥1}, where {ani,1≤i≤n,n≥1} is anarray of real numbers. By replacing the sequence of positive integers {mn,n≥1} in Rita GiulianoAntonini.etc(2001) theorem 1 by the natural sequence n≥1, and extending independent randomvariables into NA random variables, m-NA random variables, two similar results with the case ofindependent random variable are derived. In addition, we also discuss the complete convergencefor weighted sums of m-NA random variables under the two cases, E|Xn|p <∞(1≤p≤2) andEXn2 <∞, with the di?erent conditions of the array of real numbers {ani,1≤i≤n,n≥1}.