Conditionings and path decompositions for Lévy processes

We first give an interpretation for the conditioning to stay positive (respectively, to die at 0) for a large class of Lévy processes starting at x > 0. Next, we specify the laws of the pre-minimum and post-minimum parts of a Lévy process conditioned to stay positive. We show that, these parts ar...

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Bibliographic Details
Published in:Stochastic processes and their applications 1996-11, Vol.64 (1), p.39-54
Main Author: Chaumont, L.
Format: Article
Language:English
Subjects:
Conditioning to stay positive
Lévy process
Lévy process Reflected process Conditioning to stay positive Path decomposition
Path decomposition
Reflected process
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Summary:We first give an interpretation for the conditioning to stay positive (respectively, to die at 0) for a large class of Lévy processes starting at x > 0. Next, we specify the laws of the pre-minimum and post-minimum parts of a Lévy process conditioned to stay positive. We show that, these parts are independent and have the same law as the process conditioned to die at 0 and the process conditioned to stay positive starting at 0, respectively. Finally, in some special cases, we prove the Skorohod convergence of this family of laws when x goes to 0.
ISSN:0304-4149
1879-209X
DOI:10.1016/S0304-4149(96)00081-6