Radonification of a cylindrical Lévy process

Abstract

In this work we present a direct proof about radonification of a cylindrical Lévy 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 Lévy process.