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

TL;DR

This paper investigates conditions under which exponential integrals of independent increment processes are generalized gamma convolutions, extending known results about their infinite divisibility and selfdecomposability.

Contribution

It provides new sufficient conditions for exponential integrals to be generalized gamma convolutions, broadening the understanding of their distributional properties.

Findings

Distributions of exponential integrals can be generalized gamma convolutions under certain conditions.

Examples illustrate the applicability of the theoretical results.

Conditions for selfdecomposability and infinite divisibility are extended to more general processes.

Abstract

It is known that in many cases distributions of exponential integrals of Levy 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.