Stochastic integral representations of F-selfdecomposable and F-semi-selfdecomposable distributions

Abstract

We study two specific mappings defined on the class of infinitely divisible distributions on Z + with finite log-moments. As a consequence, we re-derive some known stochastic integral representations for Fselfdecomposable distributions and obtain some new ones for F-semi-selfdecomposable distributions. Stochastic integral representations for discrete distributions in nested subclasses of F-selfdecomposable and F-semi-selfdecomposable distributions are established via the iterates of the aforementioned mappings.