On the Error of the Gaussian Approximation for Convolutions
On the Error of the Gaussian Approximation for Convolutions
复制标题
关于卷积高斯近似的误差
DOI：
10.1137/1122030
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发表时间：
1978
影响因子：
0.6
通讯作者：
V. V. Yurinskii
中科院分区：
文献类型：
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作者：
V. V. Yurinskii
设1，””，n Rk是具有有限三阶矩的独立随机向量，设Fn是：1-[-”-[-：n的分布，设Gn是具有与Fn相同的一阶和二阶矩的高斯分布。此外，让我。是Rk（满足描述范数的公理系统，但对x 0可为零）中的一个范数，令n（F，G）是分布F和G之间的L 6vy-Prokhorov距离，借助于[. [，即正数集合e的最大下界，使得
Let 1,’’’, n Rk be independent random vectors with finite third mo-ments, let Fn be the distribution of: 1-[-"""-[-: n, andlet Gn be the Gaussian distribution with the same first and second moments as Fn. Moreover, let l. be a seminorm in Rk (Ix [satisfies the system of axioms describing a norm, but can vanish for x 0), and let n (F, G) be the L6vy-Prokhorov distance between the distributions F and G, defined with thehelp of [.[, ie, the greatest lower bound of the set of positive numbers e such that