Product systems arising from Lévy processe

Abstract

This paper investigates the structure of product systems of Hilbert spaces derived from Banach space-valued Lévy processes. We establish conditions under which these product systems are completely spatial and show that Gaussian Lévy processes with non-degenerate covariance always give rise to product systems of type I. Furthermore, we construct a continuum of non-isomorphic product systems of type \(\rm{II}\sb\infty\) from pure jump Lévy processes.

minor revisions and typographical corrections