## Regularity of the Cauchy principal value of the local times of some Lévy processes.(English)Zbl 0922.60073

Roughly speaking, the Cauchy principal value of the local times of a real-valued Lévy process $$X=(X_t, t\geq 0)$$ is given by $$C_t=\text{p.v. } \int^t_0 {ds\over X_s}$$, $$t\geq 0$$, where the notation p.v. refers to principal value. The purpose of this paper is to investigate the regularity of the Cauchy principal value $$C$$ of the local times of certain Lévy processes with no negative jumps. The authors define $$C$$ under the weakest possible conditions and show that this process always has continuous sample paths. Moreover, the authors specify the real numbers $$p>1$$ for which $$C$$ has finite $$p$$-variation.
Reviewer: Z.Rychlik (Lublin)

### MSC:

 60J99 Markov processes 60J55 Local time and additive functionals 60G17 Sample path properties
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### References:

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