Several Convergence Theorems Of The Sums Of Random Variables

The main purpose of this paper is to study the convergence problem some special functions.The first chapter, we give the introduction, include some of the major concepts and the existing classical results.In the second chapter, we shall establish a new almost sure convergence theorem for the negatively associated sequence, the classic Marcinkiewicz-Zygmund strong law of large numbers is deduced. We further point out that the above moment condition is also necessary for the almost sure convergence.The third chapter discusses a special weighted sums: have almost sure convergence properties, and the equivalence of the almost sure and complete convergence of μn is proved.(under normal circumstances, by the Borel-Cantelli lemma, complete convergence can be launched almost sure convergence)...