Semi-stable distributions in free probability theory

作     者：Shandong University, Ji’nan 250100, China Department of Mathematics and Statistics, Memorial University of Newfoundland, HH 3050, St. John’s, A1C 5S7, Canada 

作者机构：Shandong University Ji’nan China Department of Mathematics and Statistics Memorial University of Newfoundland St. John’s Canada 

出 版 物：《Science China Mathematics》 (中国科学：数学（英文版）)

年 卷 期：2006年第49卷第3期

页      面：387-397页

核心收录：

学科分类：02[经济学] 0202[经济学-应用经济学] 020208[经济学-统计学] 07[理学] 0714[理学-统计学（可授理学、经济学学位）] 070103[理学-概率论与数理统计] 0701[理学-数学] 

主　　题：stable distributions, semi-stable distributions, noncommutative random vari-ables, Voiculescu transform, free cumulant transform. 

摘      要：Semi-stable distributions, in classical probability theory, are characterized as limiting distributions of subsequences of normalized partial sums of independent and identically distributed random variables. We establish the noncommutative counterpart of semi-stable distributions. We study the characterization of noncommutative semi-stability through free cumulant transform and develop the free semi-stability and domain of semi-stable attraction in free probability theory.