Distributions of exponential integrals of independent increment processes related to generalized gamma convolutions

Abstract

It is known that in many cases distributions of exponential integrals of Lévy processes are infinitely divisible and in some cases they are also selfdecomposable. In this paper, we give some sufficient conditions under which distributions of exponential integrals are not only selfdecomposable but furthermore are generalized gamma convolution. We also study exponential integrals of more general independent increment processes. Several examples are given for illustration.