Radonification of a cylindrical Lévy process

Abstract

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 a 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 proof to those who are not familiar with this method and also present our result which is to apply the radonification method to the case of a cylindrical Lévy process.