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

In this paper we study some linear and quasi-linear stochastic equations with the random fractional Laplacian operator driven by arbitrary Lévy processes. The driving noise can be space–time in the case of one dimensional spacial variable. We prove uniqueness and existence of such equations...