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- Title
CHARACTERIZATIONS OF THE CLASS OF FREE SELF-DECOMPOSABLE DISTRIBUTIONS AND ITS SUBCLASSES.
- Authors
SAKUMA, NORIYOSHI
- Abstract
In this paper, we firstly characterize the class of free self-decomposable distributions as a class of limiting distributions of suitably normalized partial sums of free independent random variables. Secondly, we introduce nested classes between the class of free self-decomposable distributions and that of free stable distributions, characterize them and show that the limit of the nested classes coincides with the closure of the class of free stable distributions. All results here are analogues of the results known in classical probability theory.
- Subjects
DISTRIBUTION (Probability theory); PROBABILITY theory; FREE probability theory; RANDOM variables; SET theory; MATHEMATICAL statistics
- Publication
Infinite Dimensional Analysis, Quantum Probability & Related Topics, 2009, Vol 12, Issue 1, p51
- ISSN
0219-0257
- Publication type
Article
- DOI
10.1142/S0219025709003525