Additive Processes on Nuclear Spaces

Abstract

In this work we construct general additive processes on the nuclear spaces, and prove Khintchin's formula and Paul Levy's decomposition for these processes. As applications, we construct some Ornstein-Uhlenbeck processes with jumps and solve some (stochastic) partial differential equations obtained from the transformations of these processes by a random diffeomorphism corresponding to a finite dimensional diffusion process.