2005/01/12 by Paavo Salminen, Marc Yor, Salminen, Paavo +1
Decision Sciences · Economics, Econometrics and Finance · Mathematics · #60J60 #60J65 #60J70 #FOS: Mathematics #Probability (math.PR) #Probability and Risk Models #Stochastic processes and financial applications #Stochastic processes and statistical mechanics #math.PR #msc:60J60 #msc:60J65 #msc:60J70
paper · pdf · doi:10.48550/arxiv.math/0501182
24 pages, no figures
arxiv created 2005/01/12 · openalex publication_date 2005/01/12 · arxiv updated 2009/12/01 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
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∈[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 \citeyamada02 and Fitzsimmons and Getoor \citefitzsimmonsgetoor92a.