Tanaka formula for symmetric Lévy processes

Paavo P. Salminen (1) , Marc Yor (2)

1 MD - Mathematical department [Abo Finland]
2 LPMA - Laboratoire de Probabilités et Modèles Aléatoires

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}.

Mots clés: resolvent; local time; stable Lévy process; additive functional

Domaines: Probabilités [math.PR]

Paavo P. Salminen, Marc Yor. Tanaka formula for symmetric Lévy processes. 2005. ⟨hal-00003872⟩