The convergence of moments in the central limit theorem for weakly dependent random variables

Central and Local Limit Theories in Markov Dependent Random Variables

On the Complete Convergence ofWeighted Sums for Dependent Random Variables

We study the limiting behavior of weighted sums for negatively associated (NA) random variables. We extend results in Wu (1999) and a theorem in Chow and Lai (1973) for NA random variables.

A central limit theorem for triangular arrays of weakly dependent random variables

We derive a central limit theorem for triangular arrays of possibly nonstationary random variables satisfying a condition of weak dependence in the sense of Doukhan and Louhichi (1999). The proof uses an apparently new variant of the Lindeberg method where the behavior of the partial sums is compared to that of partial sums of dependent Gaussian random variables. We also discuss a few applicati...

On the Convergence Rate of the Law of Large Numbers for Sums of Dependent Random Variables

In this paper, we generalize some results of Chandra and Goswami [4] for pairwise negatively dependent random variables (henceforth r.v.’s). Furthermore, we give Baum and Katz’s [1] type results on estimate for the rate of convergence in these laws.

Central Limit Theorem in Multitype Branching Random Walk

A discrete time multitype (p-type) branching random walk on the real line R is considered. The positions of the j-type individuals in the n-th generation form a point process. The asymptotic behavior of these point processes, when the generation size tends to infinity, is studied. The central limit theorem is proved.