We prove the existence of the local time of the Ornstein–Uhlenbeck type process X={Xt,t∈R+} driven by a general Lévy process. The conditions of the continuity in time variable t and the regularity property of the local time are given, under mild regularity conditions on the driving Lévy...

Let be a Lévy process, and where . Taylor (1986) showed that the packing dimension of the trajectory of X is [gamma]0. An open question from Pruitt and Taylor (1996) is: Is it true that [gamma]0=inf{[alpha]=0:a-[alpha]T(a,1)--[infinity] a.s.  as  a--0}? In this paper, we...