Tanaka formula for symmetric L\'evy 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 L\'evy processes. The most interesting case is that of the symmetric -stable L\'evy 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 yamada02 and Fitzsimmons and Getoor fitzsimmonsgetoor92a.
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