Tanaka Formula for Symmetric Levy 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 Levy processes. The most interesting case is that of the symmetric alpha-stable Levy process (for alpha is an element of (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].