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Product systems arising from Lévy processe
Remus Floricel, Peter Wadel · 2024-10-19 · via math.PR updates on arXiv.org

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.

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