On quasi-convergence of series of independent 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.

Convergence of series of dependent φ-subgaussian random variables

The almost sure convergence of weighted sums of φ-subgaussian m-acceptable random variables is investigated. As corollaries, the main results are applied to the case of negatively dependent and m-dependent subgaussian random variables. Finally, an application to random Fourier series is presented. © 2007 Elsevier Inc. All rights reserved.

Almost sure convergence of weighted sums of independent random variables

Let (Ω,F ,P) be a probability space, and let {Xn} be a sequence of integrable centered i.i.d. random variables. In this paper we consider what conditions should be imposed on a complex sequence {bn} with |bn| → ∞, in order to obtain a.s. convergence of P n Xn bn , whenever X1 is in a certain class of integrability. In particular, our condition allows us to generalize the rate obtained by Marcin...

Dominated Convergence for Fuzzy Random Variables

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.