Convergence of weighted averages of random variables revisited
Convergence of weighted averages of random variables revisited
复制标题
重新审视随机变量加权平均值的收敛性
DOI：
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发表时间：
2006
期刊：
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通讯作者：
Nasrollah Etemadi
中科院分区：
文献类型：
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作者：
Nasrollah Etemadi
我们证明了对于一个大类的正权重，包括最终单调递减的和最终单调递增但规则变化的权重，如果随机变量的平均值在某种意义上收敛，那么它们对应的加权平均值也在相同的意义上收敛。我们还将替换Jamison、Pruitt和Orey的基本结果中的充分条件，使i.i.d.随机变量，使他们的工作更加透明。
We show that for a large class of positive weights including the ones that are eventually monotone decreasing and those that are eventually monotone increasing but vary regularly, if the averages of random variables converge in some sense, then their corresponding weighted averages also converge in the same sense. We will also replace the sufficient conditions in the fundamental result of Jamison, Pruitt, and Orey for i.i.d. random variables that make their work more transparent.