Completely random measures and Levy bases in free probability

被引：0
|
作者：
Collet, Francesca [1 ]
Leisen, Fabrizio [2 ]
Thorbjornsen, Steen [3 ]
机构：
[1] Univ Padua, Dept Math, Via Trieste 63, I-35121 Padua, Italy
[2] Univ Nottingham, Sch Math Sci, Univ Pk, Nottingham NG7 2RD, England
[3] Univ Aarhus, Dept Math, Ny Munkegade 118, DK-8000 Aarhus C, Denmark
来源：
ELECTRONIC JOURNAL OF PROBABILITY | 2021年 / 26卷
关键词：
free completely random measure; free infinite divisibility; free Levy basis; Levy-Ito type decomposition;
D O I：
10.1214/21-EJP620
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：
This paper develops a theory for completely random measures in the framework of free probability. A general existence result for free completely random measures is established, and in analogy to the classical work of Kingman it is proved that such random measures can be decomposed into the sum of a purely atomic part and a (freely) infinitely divisible part. The latter part (termed a free Levy basis) is studied in detail in terms of the free Levy-Khintchine representation and a theory parallel to the classical work of Rajput and Rosinski is developed. Finally a Levy-Ito type decomposition for general free Levy bases is established.
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页数：41
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