A criterion of quasi-infinite divisibility for discrete laws

TL;DR

This paper introduces a new criterion to determine whether discrete probability laws are quasi-infinitely divisible, extending the class of infinitely divisible laws via Lévy-type representations.

Contribution

It provides a novel criterion for classifying discrete laws as quasi-infinitely divisible, broadening the understanding of their structure beyond traditional infinitely divisible laws.

Findings

Established a criterion for quasi-infinite divisibility of discrete laws

Extended the class of infinitely divisible laws through Lévy-type representations

Provided theoretical foundations for further research in probability laws

Abstract

We consider arbitrary discrete probability laws on the real line. We obtain a criterion of their belonging to a new class of quasi-infinitely divisible laws, which is a wide natural extension of the class of well known infinitely divisible laws through the L\'evy type representations.