Bernoulli

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  • 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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Abstract

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.

Article information

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

Dates
First available in Project Euclid: 22 March 2004

Permanent link to this document
https://projecteuclid.org/euclid.bj/1080004766

Mathematical Reviews number (MathSciNet)
MR2002f:60090

Zentralblatt MATH identifier
1003.60045

Keywords
excursion measure fluctuation theory Lévy processes local time

Citation

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


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References

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