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Zbl 0876.60060
Bertoin, Jean; Yor, Marc
Some independence results related to the arc-sine law.
(English)
[J] J. Theor. Probab. 9, No.2, 447-458 (1996). ISSN 0894-9840; ISSN 1572-9230/e

This paper is devoted to the proof of recent results of Getoor and Sharpe on the distribution of local times on rays for planar Lévy processes $(X,Y)$. The main interest is on the local time $l$ of $Y$ and the process $L_t=\int^t_0 1_{\{X_s>0\}}dl_s$. It is proved that for every time $t>0$, $l_t$ and $L_t/l_t$ are independent and the latter is distributed according to a generalized arc-sine law. An asymptotic result concerning the law of $L_t$ is proved as well.
[D.Lepingle (Orléans)]
MSC 2000:

Keywords: local times; Lévy processes; generalized arc-sine law

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