Georgia Institute of Technology College of Sciences

We obtain an extension of the Ito-Nisio theorem to certain non separable Banach spaces and apply it to the continuity of the Ito map and Levy processes. The Ito map assigns a rough path input of an ODE to its solution (output). Continuity of this map usually requires strong, non separable, Banach space norms on the path space. We consider as an input to this map a series expansion a Levy process and study the mode of convergence of the corresponding series of outputs. The key to this approach is the validity of Ito-Nisio theorem in non separable Wiener spaces of certain functions of bounded p-variation. This talk is based on a joint work with Andreas Basse-O’Connor and Jorgen Hoffmann-Jorgensen.