Time regularity of solutions to linear equations with Lévy noise in infinite dimensions

The existence of strong and weak càdlàg versions of a solution to a linear equation in a Hilbert space HH, driven by a Lévy process taking values in a Hilbert space U↩HU↩H is established. The so-called cylindrical càdlàg property is investigated as well. A special emphasis is put on infinite systems of linear equations driven by independent Lévy processes.