A potential theoretic approach to Tanaka formula for asymmetric Lévy processes

2016/09/01 by Hiroshi Tsukada, Tsukada, Hiroshi · 1 citation
Decision Sciences · Economics, Econometrics and Finance · Mathematics · #FOS: Mathematics #Probability (math.PR) #Probability and Risk Models #Statistical Distribution Estimation and Applications #Stochastic processes and financial applications

paper · pdf · doi:10.48550/arxiv.1609.00082

openalex publication_date 2016/09/01 · openalex created_date 2025/10/10 · openalex updated_date 2026/08/04

Abstract

In this paper, we shall introduce the Tanaka formula from viewpoint of the Doob-Meyer decomposition. For symmetric Lévy 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 α∈ (1,2), we studied the Tanaka formula by using Itô's stochastic calculus and the Fourier analysis. In this paper, we study the Tanaka formula for asymmetric Lévy 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 Lévy processes and it generalized the result in Yano (2013).

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