scholarly journals Stochastic calculus and the continuity of local times of Lévy processes

1992 ◽  
pp. 1-10
Author(s):  
Richard Bass ◽  
Davar Khoshnevisan
Keyword(s):  
Lévy Processes ◽  
Levy Processes ◽  
Stochastic Calculus ◽  
Local Times

scholarly journals Tanaka formula for strictly stable processes

2019 ◽  
Vol 39 (1) ◽  
pp. 39-60
Author(s):  
Hiroshi Tsukada
Keyword(s):  
Potential Theory ◽  
Lévy Processes ◽  
Levy Processes ◽  
Stochastic Calculus ◽  
Local Times ◽  
Stable Processes ◽  
Tanaka Formula

For symmetric Levy processes, if the local times exist, the Tanaka formula has already been constructed via the techniques in the potential theory by Salminen and Yor 2007. In this paper, we study the Tanaka formula for arbitrary strictly stable processes with index α ∈ 1, 2, including spectrally positive and negative cases in a framework of Ito’s stochastic calculus. Our approach to the existence of local times for such processes is different from that of Bertoin 1996.

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