Conditionings and path decompositions for Lévy processes

L. Chaumont

Stochastic Processes and their Applications, 1996, vol. 64, issue 1, 39-54

Abstract: 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.

Keywords: Lévy; process; Reflected; process; Conditioning; to; stay; positive; Path; decomposition (search for similar items in EconPapers)
Date: 1996
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Citations: View citations in EconPapers (11)

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