Radonification of a cylindrical L\'evy process

TL;DR

This paper provides a straightforward proof of radonification for cylindrical Lévy processes, enabling the construction of genuine stochastic processes from cylindrical ones using Hilbert-Schmidt operators.

Contribution

It offers a self-contained, simple proof of radonification for cylindrical Lévy processes, expanding the applicability of the method.

Findings

Radonification of cylindrical Lévy processes established

Simplified proof accessible to non-experts

Application of radonification to cylindrical Lévy processes

Abstract

In this work we present a direct proof about radonification of a cylindrical L\'evy process. The radonification technique has been very useful to define an genuine stochastic process starting from a cylindrical process, this is possible thanks to the Hilbert-Schmidt operators. With this work we want to propose a self-contained simple proofs who those who are not familiar with this method, and also present our result which it is apply the radonification method to the case of a cylindrical L\'evy process.