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设{Xni,un≤i≤vn,n≥1}与{ani,un≤i≤vn,n≥1}分别为一个随机阵列和一个常数阵列.本文首先引入了随机阵列{Xni,un≤i≤vn,n≥1}关于常数阵列{ani,un≤i≤vn,n≥1}剩余h-可积的概念,它是弱于h-可积,Cesaroα-可积等其它相关可积的定义.然后在这一可积的定义和适当的条件下,我们研究了相依随机序列加权和的强收敛性和平均收敛性,推广并改进了相关文献已有结果.

Convergence for Weighted Sums of Dependent Random Variables under Residual h-Integrability Assumption

Let be an array of random variables and be an array of
constants. A new concept of integrability (call residually
-integrability) for an array of random variableswith respect to an array of constants is introduced,
which is weaker than other related notions of integrability, such as
-integrability, -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.