Radonifying operators and infinitely divisible Wiener integrals

TL;DR

This paper explores the connection between radonifying operators and Wiener integrals with respect to Levy processes in Banach spaces, introducing theta-radonifying operators to extend Gaussian results.

Contribution

It introduces theta-radonifying operators and analyzes their role in defining Wiener integrals for infinitely divisible cylindrical measures, expanding the theory beyond Gaussian cases.

Findings

Characterization of theta-radonifying operators for various measures

Differences identified between Gaussian and infinitely divisible cases

Conditions established for the existence of Wiener integrals in Banach spaces

Abstract

In this article we illustrate the relation between the existence of Wiener integrals with respect to a Levy process in a separable Banach space and radonifying operators. For this purpose, we introduce the class of theta-radonifying operators, i.e. operators which map a cylindrical measure theta to a genuine Radon measure. We study this class of operators for various examples of infinitely divisible cylindrical measures theta and highlight the differences from the Gaussian case.