Quelques nouvelles identités de fluctuation pour les processus de Lévy

Abstract

Let τ and H be the ladder time and ladder height processes of a 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. The later allows us to get a relationship between the entrance law of X and the entrance law of the excursion measure away from 0 of the reflected process (X t- inf s≤ X s >- 0). In the stable case, some explicit calculations are provided.