Levy-LePage series representation of stable vectors: Convergence in variation

被引：7

作者：

Bentkus, V

Juozulynas, A

Paulauskas, V

机构：

[1] Inst Math & Informat, LT-2000 Vilnius, Lithuania

[2] Vilnius State Univ, Dept Math, LT-2006 Vilnius, Lithuania

来源：

JOURNAL OF THEORETICAL PROBABILITY | 2001年 / 14卷 / 04期

关键词：

stable laws; Poissonian representation; Levy LePage series; convergence in variation; convergence rates;

D O I：

10.1023/A:1017520702943

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：

Multidimensional stable laws G(alpha) admit a well-known Levy-LePage series representation G(alpha)=L(Sigma (alpha)(j=1)Gamma X--1/alpha(j)j), 0 < alpha <2 where Gamma (1), Gamma (2), .... are the successive times of jumps of a standard Poisson process, and X-1, X-2,.... denote i.i.d. random vectors, independent of Gamma (1), Gamma (2),.... We present (asymptotically) optimal bounds for the total variation distance between a stable law and the distribution of a partial sum of the Levy-LePage series. In the one-dimensional case similar results were obtained earlier by Bentkus, Gotze, and Paulauskas.

引用

页码：949 / 978

页数：30

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