Complete convergence for weighted sums of a class of random variables

Abstract

Let {a ni , 1 ≤ i ≤ n, n ≥ 1} be an array of real numbers and {X n , n ≥ 1} be a sequence of random variables satisfying the Rosenthal type inequality, which is stochastically dominated by a random variable X. Under mild conditions, we present some results on complete convergence for weighted sums n i=1 a ni X i of random variables satisfying the Rosenthal type inequality. The results obtained in the paper generalize some known ones in the literatures. ∞ n=1 P(|X n − θ| > ε) < ∞.

New Approach to Proximity Analysis Between Two Horizontal Multi-Tables: Dscia2 Method

“…Under mild condition we establish the complete convergence for weighted sums j i=1 Ψ ni X i . This result obtained with random coefficients generalizes the work of those obtained with real coefficients [12][13][14]16]. Our results also generalize those on complete convergence theorem previously obtained from the independent and identically distributed case to negatively dependent.…”

Complete convergence for weighted sums of pairwise independent random variables

“…For the negatively orthant dependent random variables, Gan and Chen [12] discussed the complete convergence of weight sums, and for some special weighted sums, Chen and Sung [13] gave necessary and sufficient conditions for the complete convergence. Deng et al [14], Zhao et al [15] presented some results on complete convergence for weighted sums of random variables satisfying the Rosenthal type inequality. Xue et al [16], Wang et al [17], Deng et al [18] studied the complete convergence for weighted sums of negatively superadditive-dependent random variables.…”

On the complete convergence for weighted sums of a class of random variables

“…1 College of Mathematics and Information Science, Henan Normal University, Xinxiang, Henan 453007, China.…”