A note on new classes of infinitely divisible distributions on $\mathbb{R}^d$

Abstract

This paper introduces and studies a family of new classes of infinitely divisible distributions on $\mathbb{R}^d$ with two parameters. Depending on parameters, these classes connect the Goldie-Steutel-Bondesson class and the class of generalized type $G$ distributions, connect the Thorin class and the class $M$, connect the class $M$ and the class of generalized type $G$ distributions. These classes are characterized by stochastic integral representations with respect to Lévy processes.