Tanaka formula for symmetric Lévy processes

Abstract

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 $\al$-stable Lévy process (for $\al\in[1,2]$) 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 \cite{yamada02} and Fitzsimmons and Getoor \cite{fitzsimmonsgetoor92a}.