CENTRAL-LIMIT-THEOREM BY POLYNOMIAL DEPENDENCE COEFFICIENTS

被引：3

作者：

BLACHER, R ^{[1
]}

机构：

[1] IMAG LAB GRENOBLE, LMC, EQUIPE SMS, F-38041 GRENOBLE, FRANCE

来源：

JOURNAL OF COMPUTATIONAL AND APPLIED MATHEMATICS | 1995年 / 57卷 / 1-2期

关键词：

ORTHOGONAL POLYNOMIALS; CENTRAL LIMIT THEOREM; FOURIER TRANSFORM;

D O I：

10.1016/0377-0427(93)E0233-C

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

We study the asymptotic behaviour of normalized sums of n random variables Sigma(n) = n (-1/2)(X(1) + X(2) + ... + X(n)). We obtain a necessary and sufficient condition in order that the moments of Sigma(n) converge to the moments of a normal distribution. This condition is expressed by means of polynomial dependence coefficients rho(j1,j2) (...) (,jn). Then, one can obtain central limit theorems with minimal assumptions.

引用

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页码：45 / 56

页数：12

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