On Free Generalized Inverse Gaussian Distributions

被引：4

作者：

Hasebe, Takahiro ^{[1
]}

Szpojankowski, Kamil ^{[2
]}

机构：

[1] Hokkaido Univ, Dept Math, Sapporo, Hokkaido, Japan

[2] Warsaw Univ Technol, Fac Math & Informat Sci, Warsaw, Poland

来源：

COMPLEX ANALYSIS AND OPERATOR THEORY | 2019年 / 13卷 / 07期

关键词：

FREE INFINITE-DIVISIBILITY; SELF-DECOMPOSABILITY; PROPERTY; LAWS;

D O I：

10.1007/s11785-018-0790-9

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

We study here properties of free Generalized Inverse Gaussian distributions (fGIG) in free probability. We show that in many cases the fGIG shares similar properties with the classical GIG distribution. In particular we prove that fGIG is freely infinitely divisible, free regular and unimodal, and moreover we determine which distributions in this class are freely selfdecomposable. In the second part of the paper we prove that for free random variables X, Y where Y has a free Poisson distribution one has X=(d) 1/X+Y if and only if X has fGIG distribution for special choice of parameters. We also point out that the free GIG distribution maximizes the same free entropy functional as the classical GIG does for the classical entropy.

引用

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页码：3091 / 3116

页数：26

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