Some Laws Of Large Numbers For Sequences Of NA And B-valued Quasi-martingale Difference

The definition of negatively associated was advanced in 1981. Form then on, many scholars have discussed the limit properties of negatively associated random variables because of its abroad application to multivariate analysis and other fields. There are many results until now, and some of them show that its limit properties are very similar to those of independence. We try to discuss its further properties in this thesis.In chapter one, we introduce the definition of negatively associated random variables, main results which were proved by scholars before, the definition of complete convergence and the forms which we are interested in.Kuczmaszewska(2005) proved a maximal inequality for fourth moment of negatively associated random variables, then derived the strong law of large numbers. In chapter two we derive the similar strong law of large numbers for 1 < r ≤ 2 and r > 2 .respectively, by using the inequalities in Shao(2000).In chapter three, we derive a maximal inequality by combining the methods in Shao(2000) and Liu(1998) without the hypothesis zero mean and the existence of the second moment, then we discuss the complete convergence for negatively associated triangular arrays by using it.In chapter four, we discuss the convergence and the weak law of large numbers forweighted sums of the form (?)a_njd_jX, where {Xn, n ≥ 1} is B-valued quasi-martingaleand {a_nj, 1≤ j ≤ k_n ↑∞,n ≥ 1} (?) R. Moreover, we discuss the convergence for randomly weighted sums of B-valued martingale difference series.