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Functional limit theorems for Lévy processes satisfying Cramér's condition


Bertoin, J; Barczy, M (2011). Functional limit theorems for Lévy processes satisfying Cramér's condition. Electronic Journal of Probability, 16:2020 -2038.

Abstract

We consider a Lévy process that starts from x<0 and conditioned on having a positive maximum. When Cramér's condition holds, we provide two weak limit theorems as x goes to −∞ for the law of the (two-sided) path shifted at the first instant when it enters (0,∞), respectively shifted at the instant when its overall maximum is reached. The comparison of these two asymptotic results yields some interesting identities related to time-reversal, insurance risk, and self-similar Markov processes.

Abstract

We consider a Lévy process that starts from x<0 and conditioned on having a positive maximum. When Cramér's condition holds, we provide two weak limit theorems as x goes to −∞ for the law of the (two-sided) path shifted at the first instant when it enters (0,∞), respectively shifted at the instant when its overall maximum is reached. The comparison of these two asymptotic results yields some interesting identities related to time-reversal, insurance risk, and self-similar Markov processes.

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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:24 Apr 2013 14:34
Last Modified:05 Apr 2016 16:43
Publisher:Institute of Mathematical Statistics
ISSN:1083-6489
Free access at:Publisher DOI. An embargo period may apply.
Publisher DOI:https://doi.org/10.1214/EJP.v16-930

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