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Article overview
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A potential theoretic approach to Tanaka formula for asymmetric L'evy processes | Hiroshi Tsukada
; | Date: |
1 Sep 2016 | Abstract: | In this paper, we shall introduce the Tanaka formula from viewpoint of the
Doob-Meyer decomposition. For symmetric L’evy processes, if the local time
exists, Salminen and Yor (2007) obtained the Tanaka formula by using the
potential theoretic techniques. On the other hand, for asymmetric stable
processes with index $alpha in (1,2)$, we studied the Tanaka formula by using
It^o’s stochastic calculus and the Fourier analysis. In this paper, we study
the Tanaka formula for asymmetric L’evy processes via the potential theoretic
approach. We give several examples for important processes. Our approach also
gives the invariant excessive function with respect to the killed process in
the case of asymmetric L’evy processes and it generalized the result in Yano
(2013). | Source: | arXiv, 1609.0082 | Services: | Forum | Review | PDF | Favorites |
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