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2005 On Lévy processes conditioned to stay positive.
Loïc Chaumont, Ronald Doney
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Electron. J. Probab. 10: 948-961 (2005). DOI: 10.1214/EJP.v10-261

Abstract

We construct the law of Lévy processes conditioned to stay positive under general hypotheses. We obtain a Williams type path decomposition at the minimum of these processes. This result is then applied to prove the weak convergence of the law of Lévy processes conditioned to stay positive as their initial state tends to 0. We describe an absolute continuity relationship between the limit law and the measure of the excursions away from 0 of the underlying Lévy process reflected at its minimum. Then, when the Lévy process creeps upwards, we study the lower tail at 0 of the law of the height of this excursion.

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Loïc Chaumont. Ronald Doney. "On Lévy processes conditioned to stay positive.." Electron. J. Probab. 10 948 - 961, 2005. https://doi.org/10.1214/EJP.v10-261

Information

Accepted: 14 July 2005; Published: 2005
First available in Project Euclid: 1 June 2016

zbMATH: 1109.60039
MathSciNet: MR2164035
Digital Object Identifier: 10.1214/EJP.v10-261

Subjects:
Primary: 60G51
Secondary: 60G17

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