Limit theorems in free probability theory.: I

被引：42
作者：
Chistyakov, G. P. [1 ]
Goetze, F. [2 ]
机构：
[1] Natl Acad Sci Ukraine, Inst Low Temp Phys & Engn, UA-61103 Kharkov, Ukraine
[2] Univ Bielefeld, Fac Math, D-33501 Bielefeld, Germany
来源：
ANNALS OF PROBABILITY | 2008年 / 36卷 / 01期
关键词：
free random variables; Cauchy transforms; free convolutions; limit theorems;
D O I：
10.1214/009117907000000051
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：
Based on an analytical approach to the definition of additive free convolution on probability measures on the real line, we prove free analogues of limit theorems for sums for nonidentically distributed random variables in classical probability theory.
引用
收藏
页码：54 / 90
页数：37
相关论文
共 36 条
[1]  
Akhiezer N. I., 1965, LECT APPROXIMATION T
[2]  
AKHIEZER NI, 1963, THEORY LINEAR OPERAT
[3]   A connection between free and classical infinite divisibility [J].
Barndorff-Nielsen, OE ;
Thorbjornsen, S .
INFINITE DIMENSIONAL ANALYSIS QUANTUM PROBABILITY AND RELATED TOPICS, 2004, 7 (04) :573-590
[4]   Levy processes in free probability [J].
Barndorff-Nielsen, OE ;
Thorbjornsen, S .
PROCEEDINGS OF THE NATIONAL ACADEMY OF SCIENCES OF THE UNITED STATES OF AMERICA, 2002, 99 (26) :16576-16580
[5]  
Barndorff-Nielsen OE, 2002, BERNOULLI, V8, P323
[6]   Partially defined semigroups relative to multiplicative free convolution [J].
Belinschi, ST ;
Bercovici, H .
INTERNATIONAL MATHEMATICS RESEARCH NOTICES, 2005, 2005 (02) :65-101
[7]   Atoms and regularity for measures in a partially defined free convolution semigroup [J].
Belinschi, ST ;
Bercovici, H .
MATHEMATISCHE ZEITSCHRIFT, 2004, 248 (04) :665-674
[8]   The atoms of the free multiplicative convolution of two probability distributions [J].
Belinschi, ST .
INTEGRAL EQUATIONS AND OPERATOR THEORY, 2003, 46 (04) :377-386
[9]  
BELINSCHI ST, 2006, LEBESGUE DECOMPOSITI
[10]   Stable laws and domains of attraction in free probability theory [J].
Bercovici, H ;
Pata, V .
ANNALS OF MATHEMATICS, 1999, 149 (03) :1023-1060
1234