Tanaka Formula for Symmetric Lévy Processes

Starting from the potential theoretic definition of the local times of a Markov process – when these exist – we obtain a Tanaka formula for the local times of symmetric Lévy processes. The most interesting case is that of the symmetric ?-stable Lévy process (for ? ∈ (1, 2]) which is studied in detail. In particular, we determine which powers of such a process are semimartingales. These results complete, in a sense, the works by K. Yamada [19] and Fitzsimmons and Getoor [8]. AMS Classification: 60J65, 60J60, 60J70 Key words: Resolvent, Local time, Stable Lévy process, Additive functional