Infinitely divisible cylindrical measures on Banach spaces

TL;DR

This paper introduces and characterizes infinitely divisible cylindrical probability measures on Banach spaces, providing new insights into their properties and implications for Levy measures.

Contribution

It offers a novel characterization of infinitely divisible cylindrical measures, extending understanding beyond Radon measures on Banach spaces.

Findings

Characterization of cylindrical measures via their characteristics

Continuity properties of infinitely divisible cylindrical measures

New results on Levy measures on Banach spaces

Abstract

In this work infinitely divisible cylindrical probability measures on arbitrary Banach spaces are introduced. The class of infinitely divisible cylindrical probability measures is described in terms of their characteristics, a characterisation which is not known in general for infinitely divisible Radon measures on Banach spaces. Further properties of infinitely divisible cylindrical measures such as continuity are derived. Moreover, the result on the classification enables us to conclude new results on genuine Levy measures on Banach spaces.