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Tanaka formula for symmetric Lévy processes

Paavo Salminen·Marc Yor
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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}.

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Paavo Salminen, Marc Yor. 2005-01-12. Tanaka formula for symmetric Lévy processes. https://arxiv.org/abs/math/0501182

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