Hajek-Renyi-Type Inequality And Strong Law Of Large Numbers On Sums Of Random Variables

Convergence and strong law of large numbers for positively associated sequences, negatively associated sequences has been deeply discussed in all kinds of paper. This paper will mainly discuss Hajeck—Renyi—Type inequality under second moment conditions for the PA sequences, NA sequences and the L~r -mixingale sequences. It generalizes the Prakasa Rao's result for positively associated sequences.This paper has four parts. Induction gives the origin of problem and some definitions and some lemmas and the conditions for the later theorem. In the second chapter, we give the proof of Hajeck—Renyi—Type inequality under second moment conditions and its applications. In the third chapter, we obtain some applications for the PA sequences , NA sequences and the L~r -mixingale sequences. In the fourth chapter we point out and correct Prakasa Rao's mistaken in paper[2].