On the self-decomposability of Euler's Gamma function
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.
scientific article; zbMATH DE number 2108258