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Some independence results related to the arc-sine law. (English) Zbl 0876.60060
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 = 0 t 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.
MSC:
60J55Local time, additive functionals
References:
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