The local time of the Markov processes of Ornstein–Uhlenbeck type

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 tt and the regularity property of the local time are given, under mild regularity conditions on the driving Lévy process. These results give information about the local properties of sample functions of the process.