Intemperate Levy Processes and White Noises

The distributional support of Levy 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 Levy white noise. The white noise associated to a class of Levy processes without support in S', 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 Levy processes.