# Some applications of duality for Lévy processes in a half-line

Abstract : The central result of this paper is an analytic duality relation for real-valued Lévy processes killed upon exiting a half-line. By Nagasawa's theorem, this yields a remarkable time-reversal identity involving the Lévy process conditioned to stay positive. As examples of applications, we construct a version of the Lévy process indexed by the entire real line and started from $-\infty$ which enjoys a natural spatial-stationarity property, and point out that the latter leads to a natural Lamperti-type representation for self-similar Markov processes in $(0,\infty)$ started from the entrance point $0+$.
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Preprints, Working Papers, ...
2009
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Cited literature [20 references]

https://hal.archives-ouvertes.fr/hal-00437716
Contributor : Jean Bertoin <>
Submitted on : Tuesday, December 1, 2009 - 11:55:14 AM
Last modification on : Tuesday, October 11, 2016 - 3:21:05 PM
Document(s) archivé(s) le : Thursday, June 17, 2010 - 6:48:38 PM

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• HAL Id : hal-00437716, version 1
• ARXIV : 0912.0131

### Citation

Jean Bertoin, Mladen Savov. Some applications of duality for Lévy processes in a half-line. 2009. 〈hal-00437716〉

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