Complete Moment Convergence for Negatively Dependent Sequences of Random Variables
نویسندگان
چکیده
منابع مشابه
Complete Convergence for Negatively Dependent Sequences of Random Variables
for all x, y ∈ R. Moreover, it follows that 1.2 implies 1.1 , and hence, 1.1 and 1.2 are equivalent. Ebrahimi and Ghosh 1 showed that 1.1 and 1.2 are not equivalent for a collection of 3 or more random variables. They considered random variables X1, X2, and X3 where X1, X2, X3 assumed the values 0, 1, 1 , 1, 0, 1 , 1, 1, 0 , and 0, 0, 0 each with probability 1/4. The random variables X1, X2, an...
متن کاملComplete 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...
متن کاملComplete 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...
متن کاملOn 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.
متن کاملComplete Moment Convergence and Mean Convergence for Arrays of Rowwise Extended Negatively Dependent Random Variables
The authors first present a Rosenthal inequality for sequence of extended negatively dependent (END) random variables. By means of the Rosenthal inequality, the authors obtain some complete moment convergence and mean convergence results for arrays of rowwise END random variables. The results in this paper extend and improve the corresponding theorems by Hu and Taylor (1997).
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ژورنال
عنوان ژورنال: Discrete Dynamics in Nature and Society
سال: 2016
ISSN: 1026-0226,1607-887X
DOI: 10.1155/2016/9039345