Complete 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 کاملThe Almost Sure Convergence for Weighted Sums of Linear Negatively Dependent Random Variables
In this paper, we generalize a theorem of Shao [12] by assuming that is a sequence of linear negatively dependent random variables. Also, we extend some theorems of Chao [6] and Thrum [14]. It is shown by an elementary method that for linear negatively dependent identically random variables with finite -th absolute moment the weighted sums converge to zero as where and is an array of...
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ژورنال
عنوان ژورنال: Journal of Inequalities and Applications
سال: 2010
ISSN: 1029-242X
DOI: 10.1155/2010/507293