On the characteristic function of the joint limit distribution of the first- and second-order power sums

被引：0

作者：

Michaletzky, G ^{[1
]}

Szeidl, L

Várlaki, P

机构：

[1] Tech Univ, Dept Telecommun & Telemat, Budapest, Hungary

[2] Eotvos Lorand Univ, Dept Probabil Theory & Stat, Budapest, Hungary

来源：

THEORY OF PROBABILITY AND ITS APPLICATIONS | 1999年 / 43卷 / 01期

关键词：

normalized power sums; domain of attraction of alpha-stable law; limit characteristic function; generalized hypergeometric functions; Fresnel S and C functions; Schrodinger equation;

D O I：

10.1137/S0040585X97976726

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：

In this paper we investigate the joint limit characteristic function of normalized first and second-order power sums for a sequence of i.i.d. random variables with distributions belonging to the domain of attraction of an alpha-stable law for alpha < 2. An explicit form is presented in terms of generalized hypergeometric functions when 0 < alpha < 2, alpha not equal 1, and that of Fresnel functions S and C for alpha = 1.

引用

页码：126 / 135

页数：10

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