Complete convergence for widely acceptable random variables under the sublinear expectations

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.

Some exponential inequalities for acceptable random variables and complete convergence

* Correspondence: volodin@math. uregina.ca Department of Mathematics and Statistics, University of Regina, Regina Saskatchewan S4S 0A2, Canada Full list of author information is available at the end of the article Abstract Some exponential inequalities for a sequence of acceptable random variables are obtained, such as Bernstein-type inequality, Hoeffding-type inequality. The Bernsteintype ineq...

Complete convergence for negatively dependent random variables

Let {Xn, n ≥ 1} be a sequence of independent and identically random variables. In 1947 Hsu and Rabbins proved that if E[X] = 0 and E[X2] < ∞, then 1 n ∑n k=1Xk converges to 0 completely. Recently, the strong convergence of weighted sums for the case of independent random variables has been discussed by Wu (1999), Hu and et. (2000, 2003) proved the complete convergence theorem for arrays of inde...

Complete Convergence for Negatively Dependent Random Variables

Let {Xn, n ≥ 1} be a sequence of i.i.d., real random variables. Hsu and Rabbins [5] proved that if E(X) = 0 and E(X) < ∞, then the sequence 1 n ∑n i=1 Xi converges to 0 completely. (i.e., the series ∑∞ n=1 P [|Sn| > nε] < ∞, converges for every ε > 0). Now let {Xn, n ≥ 1} be a sequence of negatively dependent real random variables. In this paper, we proved the complete convergence of the sequen...

Dominated Convergence for Fuzzy Random Variables