Limit theorems for free Levy processes

被引：1
作者：
Arizmendi, Octavio [1 ]
Hasebe, Takahiro [2 ]
机构：
[1] Ctr Invest Matemat, Dept Probabil & Stat, Guanajuato, Mexico
[2] Hokkaido Univ, Dept Math, Kita Ku, Kita 10,Nishi 8, Sapporo, Hokkaido 0600810, Japan
来源：
ELECTRONIC JOURNAL OF PROBABILITY | 2018年 / 23卷
关键词：
free Levy processes; multiplicative convolutions; Boolean independence; limit theorems; small times; FREE CONVOLUTION; DECOMPOSABILITY; MULTIPLICATION; ATTRACTION; OPERATORS; MONOTONE; LAWS;
D O I：
10.1214/18-EJP224
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 consider different limit theorems for additive and multiplicative free Levy processes. The main results are concerned with positive and unitary multiplicative free Levy processes at small times, showing convergence to log free stable laws for many examples. The additive case is much easier, and we establish the convergence at small or large times to free stable laws. During the investigation we found out that a log free stable law with index 1 coincides with the Dykema-Haagerup distribution. We also consider limit theorems for positive multiplicative Boolean Levy processes at small times, obtaining log Boolean stable laws in the limit.
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页数：37
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