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 ?-stable Lévy 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 [19] and Fitzsimmons and Getoor [8]. AMS Classification: 60J65, 60J60, 60J70 Key words: Resolvent, Local time, Stable Lévy process, Additive functional
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- Brownian Motion
- Local Time
- Dirichlet Process
- Springer Lecture Note
- Canonical Decomposition
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Salminen, P., Yor, M. (2007). Tanaka Formula for Symmetric Lévy Processes. In: Donati-Martin, C., Émery, M., Rouault, A., Stricker, C. (eds) Séminaire de Probabilités XL. Lecture Notes in Mathematics, vol 1899. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-540-71189-6_14
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DOI: https://doi.org/10.1007/978-3-540-71189-6_14
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