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Abstract

Let $\100dpi \inline $\{X_{ni},u_n\leqslant i\leqslant v_n, n\geqslant 1\}$$ be an array of random variables and $\100dpi \inline $\{a_{ni}, u_n\leqslant i\leqslant v_n,n\geqslant1\}$$ be an array of
constants. A new concept of integrability (call residually
$\100dpi \inline $h$$ -integrability) for an array of random variables $\100dpi \inline $\{X_{ni}\}$$ with respect to an array of constants $\100dpi \inline $\{a_{ni}\}$$ is introduced,
which is weaker than other related notions of integrability, such as
$\100dpi \inline $h$$ -integrability, $\100dpi \inline Ces\`{a}ro$ $\100dpi \inline $\alpha$$ -integrability. Under this
assumption of integrability and appropriate conditions on the array
of weights, we investigate strong convergence and mean convergence
for weighted sums of dependent random variables. Some related
results in literature are extended and improved.

Key words�� -mixing sequence, pairwise LCND random
sequence, ')" href="#"> $\100dpi \inline $\varphi$$ -mixing sequence, pairwise LCND random
sequence, -mean convergence, uniform integrability, weighted
sums.')" href="#"> $\100dpi \inline $r$$ -mean convergence, uniform integrability, weighted
sums.

Corresponding Authors: Hu Xueping

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http://aps.ecnu.edu.cn/EN/ OR http://aps.ecnu.edu.cn/EN/Y2013/V29/I1/64

[1]	Huang Haiwu, Wu Qunying, Zhang Hanjun, Ye Daxiang. On Limiting Behavior of Weighted Sums for Arrays of Rowwise \wt{\varphi}-Mixing Random Variables[J]. CHINESE JOURNAL OF APPLIED PROBABILITY AND STATIST, 2015, 31(1): 35-45.