On The Complete Convergence For Weighted Sums Of A Class Of Random Variables

In the present article, we mainly study the complete convergence of weighted sums(?) aniXi of a class of random variables satisfying the Rosenthal's inequality.The first chapter introduces the research background and the important applications of weighted sums in statistics and probability. The focus is the practical significance in statistics. The wide applications of weighted sums in statistics and probability makes the study of weighted sums of particularly importance.The second chapter introduces the related basic knowledge, such as convergence,Rosenthal's inequality, complete convergence and so on and the related lemmas and in-equalities. This chapter also includes some research results of the predecessors which has put forward a research direction and provided a good foundation for this research.In the third chapter, we discuss the complete convergence of weighted sums (?)aniXiin two different conditions, and make some generalizations. With the truncated method,Markov inequality, we obtained the convergence for weighted sums of a class of rancdom variables which satisfying Rosenthal inequality under the weaker conditions. The results improve and extend the corresponding results of the cited references.