zbMATH — the first resource for mathematics

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].

60J27 Continuous-time Markov processes on discrete state spaces
60J65 Brownian motion
Full Text: Numdam EuDML