Time regularity of Lévy-type evolution in Hilbert spaces and of some $\alpha$-stable processes

Abstract

In this paper we consider the existence of weakly càdlàg versions of a solution to a linear equation in a Hilbert space $H$, driven by a Levy process taking values in a Hilbert space $U$. In particular we are interested in diagonal type processes, where process on coordinates are functionals of independent $\alpha$ stable symmetric process. We give the if and only if characterization in this case. We apply the same techniques to obtain a sufficient condition for existence of a càdlàg versions of stable processes described as integrals of deterministic functions with respect to symmetric $\alpha$-stable random measures with $\alpha \in [1,2)$.

12 pages