Time regularity of Lévy-type evolution in Hilbert spaces and of some α-stable processes.

Abstract

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