On the self-decomposability of Euler's Gamma function
type: Item
instance of: scholarly article
title: On the self-decomposability of Euler's Gamma function
zbMATH Open document ID: 1086.33002
DOI: 10.1023/A:1026141402811
published in: Lithuanian Mathematical Journal
publication date: 2004-10-15T00:00:00Z
review text: Let \(\Gamma\) be Euler's gamma function. It is proved that, for all \(\alpha\neq0\), \(\beta>0\), \(\gamma>0\) and \(\delta>0\), the function \(\big[\Gamma(\gamma+i\alpha z)/\Gamma(\gamma)\beta^{i\alpha z}\big]^\delta\) for \(z\in\mathbb{R}\) is a self-decomposable characteristic function from the Thorin class \(\mathcal{T}_e\) and derive its explicit canonical form. Moreover, several classes of Lévy-type stochastic processes related to \(\Gamma\) are described.
reviewed by: Feng Qi
Mathematics Subject Classification ID: 33B15
Mathematics Subject Classification ID: 60E10
zbMATH DE Number: 2108258
zbMATH Keywords: Euler's gamma function
zbMATH Keywords: gamma distribution
zbMATH Keywords: Gumbel distribution
zbMATH Keywords: self-decomposability
zbMATH Keywords: self-similarity
zbMATH Keywords: Lévy process
zbMATH Keywords: Ornstein-Uhlenbeck-type process
zbMATH Keywords: Esscher transform
zbMATH Keywords: mixed exponential process
author: Bronius Grigelionis
MaRDI profile type: Publication
full work available at URL: a:1026141402811
OpenAlex ID: W135555447
description: scientific article; zbMATH DE number 2108258