On the inverse gamma subordinator

TL;DR

This paper investigates gamma subordinators and their inverse processes, providing new representations for moments and potential functions using advanced transcendental functions, and addressing open problems in the field.

Contribution

It introduces novel representations for moments and potentials of inverse gamma subordinators using Volterra functions, advancing understanding of their governing equations.

Findings

Derived explicit formulas for moments of inverse gamma subordinators.

Analyzed the governing equations related to gamma subordinators and inverse processes.

Connected representations to higher transcendental functions, enriching mathematical understanding.

Abstract

In this paper we deal with some open problems concerned with gamma subordinators. In particular, we provide a representation for the moments of the inverse gamma subordinator. Then, we focus on $\lambda$-potentials and we study the governing equations associated with gamma subordinators and inverse processes. Such representations are given in terms of higher transcendental functions, also known as Volterra functions.