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


Bertoin, J; Savov, M (2011). Some applications of duality for Lévy processes in a half-line. Bulletin of the London Mathematical Society, 43(1):97-110.

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−∞, which enjoys a natural spatial-stationarity property, and we point out that the latter leads to a natural Lamperti-type representation for self-similar Markov processes in (0, ∞) started from the entrance point 0+.

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−∞, which enjoys a natural spatial-stationarity property, and we point out that the latter leads to a natural Lamperti-type representation for self-similar Markov processes in (0, ∞) started from the entrance point 0+.

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Additional indexing

Item Type:Journal Article, refereed, original work
Communities & Collections:07 Faculty of Science > Institute of Mathematics
Dewey Decimal Classification:510 Mathematics
Language:English
Date:2011
Deposited On:14 Nov 2011 14:37
Last Modified:05 Apr 2016 15:06
Publisher:Oxford University Press
ISSN:0024-6093
Publisher DOI:https://doi.org/10.1112/blms/bdq084
Related URLs:http://arxiv.org/abs/0912.0131

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