Let $\{X_n;n\ge 1\}$ be a sequence of independent and identically distributed random variables on a sub-linear expectation space $(\Omega ,\mathscr{H},\widehat{\mathbb{E}})$, $S_n=X_1+\dots +X_n$. We consider the moments of ${max}_{n\ge 1}\left|S_n\right|/\sqrt{2nloglogn}$. The sufficient and necessary conditions for the moments to be finite are given. As an application, we obtain the law of the iterated logarithm for moving average processes of independent and identically distributed random variables.

中文翻译：

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次线性期望下与迭代对数定律相关的归一化部分和最大值的矩

让$\{X_n;n\ge 1\}$是亚线性期望空间上的独立同分布随机变量序列$(\Omega ,\mathscr{H},\widehat{\mathbb{乙}})$,${\mathrm{小号}}_n=X_1+\dots +X_n$. 我们考虑的时刻${最大限度}_{n\ge 1}\left|{\mathrm{小号}}_n\right|/\sqrt{2n日志日志n}$. 给出了矩为有限的充分必要条件。作为应用，我们得到了独立同分布随机变量的移动平均过程的迭代对数定律。