Université Paris 6
Pierre et Marie Curie | Université Paris 7
Denis Diderot | |

CNRS U.M.R. 7599
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``Probabilités et Modèles Aléatoires''
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**Auteur(s): **

**Code(s) de Classification MSC:**

- 60J30 Processes with independent increments
- 60J20 Applications of discrete Markov processes (social mobility, learning theory, industrial processes, etc.), See Also {90B30, 92H10, 92H35, 92J40}

**Résumé:** Let $\tau$ and $H$ be
respectively the ladder time and ladder height processes
associated to a given L\'evy process $X$. We give an identity in
law between $(\tau,H)$ 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 $(X_t- \inf_{s\leq t}X_s\,,\;t\geq0)$. In the stable case,
some explicit calculations are provided. These results also lead
to an explicit form of the entrance law of the L\'evy process
conditioned to stay positive.

**Mots Clés:** *Processus de Lévy ; théorie des fluctuations ; mesure d'excursion*

**Date:** 1999-03-31

**Prépublication numéro:** *PMA-584*