When addressing various financial problems, such as estimating stock portfolio risk, it is necessary to derive the distribution of the sum of the dependent random variables. Although deriving this distribution requires identifying the joint distribution of these random variables, exact estimation of the joint distribution of dependent random variables is difficult. Therefore, in recent years, studies have been conducted on the bound of the sum of dependent random variables with dependence uncertainty. In this study, we obtain an improved Hoeffding inequality for dependent bounded variables. Further, we expand the above result to the case of sub-Gaussian random variables.

中文翻译：

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改进的依赖有界或亚高斯随机变量的 Hoeffding 不等式

在解决各种财务问题时，例如估计股票投资组合的风险，有必要推导出因随机变量之和的分布。尽管推导该分布需要确定这些随机变量的联合分布，但难以准确估计因随机变量的联合分布。因此，近年来，对具有依赖不确定性的因随机变量之和的界进行了研究。在这项研究中，我们得到了一个改进的因有界变量的 Hoeffding 不等式。此外，我们将上述结果扩展到亚高斯随机变量的情况。