Complete Convergence Properties of the Sums for -mixing Sequences of Random Variables

This paper discusses complete convergence properties of the sums of -mixing random sequences.As a result,we improve the corresponding results of Wu Qunying（2001）. And extended the Baum and Katz complete convergence to the case of -mixing random sequences by moment inequality and truncating without necessarily adding any extra conditions.     

The Strong Law of Large Numbers for ■-Mixing Random Variables

In this paper we present some results for the general strong laws of large numbers of ■-mixing random variables by a maximal inequality of Utev and Peligrad.These results extend and improve the related known works in the literature.     

Inequalities of Maximum of Partial Sums and Weak Convergence for a Class of Weak Dependent Random Variables

In this paper, we establish a Rosenthal-type inequality of the maximum of partial sums for ρ^- -mixing random fields. As its applications we get the Hájeck -Rènyi inequality and weak convergence of sums of ρ^- -mixing sequence. These results extend related results for NA sequence and p^＊ -mixing random fields,     

Some Exponential Inequalities for Positively Associated Random Variables and Rates of Convergence of the Strong Law of Large Numbers

We present some exponential inequalities for positively associated unbounded random variables. By these inequalities, we obtain the rate of convergence n ^−1/2 β _n log ^3/2 n in which β _n can be particularly taken as (log log n)^1/σ with any σ>2 for the case of geometrically decreasing covariances, which is faster than the corresponding one n ^−1/2(log log n)^1/2log ² n obtained by Xing, Yang, and Liu in J. Inequal. Appl., doi: (2008) for the case mentioned above, and derive the convergence rate n ^−1/2 β _n log ^1/2 n for the above β _n under the given covariance function, which improves the relevant one n ^−1/2(log log n)^1/2log n obtained by Yang and Chen in Sci. China, Ser. A 49(1), 78–85 (2006) for associated uniformly bounded random variables. In addition, some moment inequalities are given to prove the main results, which extend and improve some known results.     

Convergence in the r－th Mean and Some Weak laws of Large Numbers for Random Weighted Sums of Random Elements in Banach Spaces

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