- Volume 7, Number 3 (2001), 557-569.
A new fluctuation identity for Lévy processes and some applications
Let τ and H be respectively the ladder time and ladder height processes associated with a given Lévy process X. We give an identity in law between (τ,H) and (X,H*), H* being the right-continuous inverse of the process H. This allows us to obtain a relationship between the entrance law of X and the entrance law of the excursion measure away from 0 of the reflected process (Xt- infs≤tXs, t ≥0). In the stable case, some explicit calculations are provided. These results also lead to an explicit form of the entrance law of the Lévy process conditioned to stay positive.
Bernoulli, Volume 7, Number 3 (2001), 557-569.
First available in Project Euclid: 22 March 2004
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Alili, Larbi; Chaumont, Loïc. A new fluctuation identity for Lévy processes and some applications. Bernoulli 7 (2001), no. 3, 557--569. https://projecteuclid.org/euclid.bj/1080004766