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.
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页码：49 / 58
页数：10
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