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

Bertoin, Jean; Caballero, Maria-Emilia

Bull. Sci. Math. 123, No. 1, 47-58 (1999).

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

Keywords:

Cauchy principal value of the local times; Lévy processes; \(p\)-variation

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