中心极限定理与丢番图逼近
Central limit theorem and Diophantine approximations
摘要：
令$F_n$表示i.i.d.的归一化和$Z_n = (X_1 + \dots + X_n)/σ\sqrt{n}$的分布函数。四阶矩有限的随机变量。本文利用$X_1$的特征函数，给出了$F_n$关于Kolmogorov距离收敛于正规律的多项式速度，以及用Edgeworth修正（$n$中的模几何增长因子）对$F_n$的多项式逼近.特殊情况下的问题进行了讨论与丢番图逼近。
英文摘要：
Let $F_n$ denote the distribution function of the normalized sum $Z_n = (X_1 + \dots + X_n)/σ\sqrt{n}$ of i.i.d. random variables with finite fourth absolute moment. In this paper, polynomial rates of convergence of $F_n$ to the normal law with respect to the Kolmogorov distance, as well as polynomial approximations of $F_n$ by the Edgeworth corrections (modulo logarithmically growing factors in $n$) are given in terms of the characteristic function of $X_1$. Particular cases of the problem are discussed in connection with Diophantine approximations.
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