On free regular and Bondesson convolution semigroups

TL;DR

This paper establishes a bijective correspondence between free regular and Bondesson convolution semigroups via complete Bernstein functions, linking free and classical subordinator distributions with explicit examples.

Contribution

It introduces a novel bijection between free regular and Bondesson convolution semigroups through complete Bernstein functions, with integral identities and examples.

Findings

Bijection between free regular and Bondesson convolution semigroups.

Integral identity linking the two classes.

Explicit examples illustrating the theoretical results.

Abstract

Free regular convolution semigroups describe the distribution of free subortinators, while Bondesson class convolution semigroups correspond to classical subordinators with completely monotone Levy density. We show that these two classes of convolution semigroups are in bijection with the class of complete Bernstein functions and we establish an integral identity linking the two semigroups. We provide several explicit examples that illustrate this result.