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On the relative lengths of excursions derived from a stable subordinator. (English) Zbl 0884.60072
Azéma, J. (ed.) et al., Séminaire de probabilités XXXI. Berlin: Springer. Lect. Notes Math. 1655, 287-305 (1997).
Summary: Results are obtained concerning the distribution of ranked relative lengths of excursions of a recurrent Markov process from a point in its state space whose inverse local time process is a stable subordinator. It is shown that for a large class of random times $$T$$ the distribution of relative excursion lengths prior to $$T$$ is the same as if $$T$$ were a fixed time. It follows that the generalized arc-sine laws of Lamperti extend to such random times $$T$$. For some other random times $$T$$, absolutely continuity relations are obtained which relate the law of the relative lengths at time $$T$$ to the law at a fixed time.
For the entire collection see [Zbl 0864.00069].

##### MSC:
 60J27 Continuous-time Markov processes on discrete state spaces 60J65 Brownian motion
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