WEAK CONVERGENCE OF SEQUENCES FROM FRACTIONAL PARTS OF RANDOM VARIABLES AND APPLICATIONS

被引：0

作者：

Giuliano, Rita ^{[1
]}

机构：

[1] Dipartimento Matemat L Tonelli, I-56100 Pisa, Italy

来源：

THEORY OF PROBABILITY AND MATHEMATICAL STATISTICS | 2010年 / 83卷

关键词：

Weak convergence; Weyl criterion; Fourier coefficient; characteristic function; partial sum; sample maximum; uniform distribution; Central Limit Theorem; domain of attraction; stable density; stable law; unimodal density; Benford's Law;

D O I：

暂无

中图分类号：

O21 [概率论与数理统计]; C8 [统计学];

学科分类号：

020208 ; 070103 ; 0714 ;

摘要：

We prove results concerning the weak convergence to the uniform distribution on [0,1] of sequences (Z(n))(n >= 1) of the form Z(n) = Y-n (mod 1)= {Y-n}, where (Y-n)(n >= 1) is a general sequence of real random variables. Applications are given: (1) to the case of partial sums of (i.i.d.) random variables having a distribution belonging to the domain of attraction of a stable law: (ii) to the case of sample maxima of i.i.d random variables.

引用

页码：49 / 58

页数：10

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