Intemperate Lévy Processes and White Noises

The distributional support of Lévy processes is important for the construction of sparse statistical models, integration in infinite dimensions and the existence of generalized solutions of stochastic partial differential equations driven by Lévy white noise. The white noise associated to a class of Lévy processes without support in \(\mathscr {S}^{\prime }\) , the space of tempered distributions, is constructed as a generalized random process. This construction also provides measures on the distribution spaces that support the paths of the Lévy processes.