English (United Kingdom)

https://curated-unify.zendy.io/wp-json/zendy-region/v1/featured_content/oa?rat=en

https://curated-unify.zendy.io/wp-json/zendy-region/v1/highlighted_journal/

Global: Zendy Plus annual

Presents the access of premium content as premium feature

Premium Content

Presents the keyphrase highlighting as premium feature

Keyphrase Highlighting

Presents the summarisation as premium feature

Summarisation

Insights

Presents the pdf analysis as premium feature

PDF Analysis

Presents the zaia usage as premium feature

ZAIA

Global: Zendy Tools annual

Global: Zendy Free Plan

Global: Zendy Tools monthly

Global: Zendy Plus monthly

In this paper, we shall introduce the Tanaka formula from viewpoint of the Doob–Meyer decomposition. For symmetric Levy processes, if the local time exists, Salminen and Yor (Tanaka formula for symmetric Levy processes. In: Seminaire de Probabilites XL. Lecture notes in mathematics, vol. 1899, Springer, Berlin, pp. 265–285, 2007) obtained the Tanaka formula by using the potential theoretic techniques. On the other hand, for strictly stable processes with index α ∈ (1, 2), we studied the Tanaka formula by using Ito’s stochastic calculus and the Fourier analysis. In this paper, we study the Tanaka formula for asymmetric Levy 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 Levy processes, and it generalized the result in Yano (J Math Ind 5(A):17–24, 2013).

A Potential Theoretic Approach to Tanaka Formula for Asymmetric Lévy Processes