| Título: | Cauchy's Principal Value of Local Times of Lévy Processes with no Negative Jumps via Continuous Branching Processes |
| Autores: | Bertoin, Jean; Université Paris VI |
| Fecha: | 1997-01-01 |
| Publicador: | Electronic journal of probability |
| Fuente: |
 |
| Tipo: |
Peer-reviewed Article |
| Tema: |
Mathematics Cauchy's principal value, Lévy process with no negative jumps, branching process. Primary: 60J30; secondary: 60F05, 60G10. |
| Descripción: | Let $X$ be a recurrent Lévy process with no negative jumps and $n$ the measure of its excursions away from $0$. Using Lamperti's connection that links $X$ to a continuous state branching process, we determine the joint distribution under $n$ of the variables $C^+_T=\int_{0}^{T}{\bf 1}_{{X_s>0}}X_s^{-1}ds$ and $C^-_T=\int_{0}^{T}{\bf 1}_{{X_s<0}}|X_s|^{-1}ds$, where $T$ denotes the duration of the excursion. This provides a new insight on an identity of Fitzsimmons and Getoor on the Hilbert transform of the local times of $X$. Further results in the same vein are also discussed. |
| Idioma: | Inglés |
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