New Classes of Infinitely Divisible Distributions Related to the Goldie-Steutel-Bondesson Class
Abstract
Recently, many classes of infinitely divisible distributions on Rd have been characterized in several ways. Among others, the first way is to use Levy measures, the second one is to use transformations of Levy measures, and the third one is to use mappings of infinitely divisible distributions defined by stochastic integrals with respect to Levy processes. In this paper, we are concerned with a class of mappings, by which we construct new classes of infinitely divisible distributions on Rd. Then we study a special case in R1, which is the class of infinitely divisible distributions without Gaussian parts generated by stochastic integrals with respect to a fixed compound Poisson processes on R1. This is closely related to the Goldie-Steutel-Bondesson class.