Complete convergence for negatively dependent random variables

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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...

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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...

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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.

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Complete Convergence for Negatively Dependent Sequences of Random Variables

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The Almost Sure Convergence for Weighted Sums of Linear Negatively Dependent Random Variables

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ژورنال

عنوان ژورنال: Journal of Applied Mathematics and Stochastic Analysis

سال: 2003

ISSN: 1048-9533,1687-2177

DOI: 10.1155/s104895330300008x