• Bernoulli
  • Volume 7, Number 3 (2001), 557-569.

A new fluctuation identity for Lévy processes and some applications

Larbi Alili and Loïc Chaumont

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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.

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Bernoulli, Volume 7, Number 3 (2001), 557-569.

First available in Project Euclid: 22 March 2004

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excursion measure fluctuation theory Lévy processes local time


Alili, Larbi; Chaumont, Loïc. A new fluctuation identity for Lévy processes and some applications. Bernoulli 7 (2001), no. 3, 557--569.

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