On a method of introducing free-infinitely divisible probability measures

TL;DR

This paper introduces a method using random integral mappings to establish isomorphisms between classical and free-infinite divisible probability measures, enabling the creation of new examples and characteristic functionals.

Contribution

It presents a novel approach using integral mappings to connect classical and free probability measures, expanding the set of known free-infinitely divisible measures.

Findings

Established isomorphisms between classical and free-infinite divisible measures.

Constructed new examples of free-infinitely divisible measures.

Developed characteristic functionals for these measures.

Abstract

Random integral mappings $I^{h,r}_{(a,b]}$ give isomorphisms between the sub-semigroups of the classical $(ID, \ast)$ and the free-infinite divisible $(ID,\boxplus)$ probability measures. This allows us to introduce new examples of such measures and their corresponding characteristic functionals.