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Functional Limit Theorems for Lévy Processes Satisfying Cramér's Condition


 
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1. Title Title of document Functional Limit Theorems for Lévy Processes Satisfying Cramér's Condition
 
2. Creator Author's name, affiliation, country Matyas Barczy; University of Debrecen; Hungary
 
2. Creator Author's name, affiliation, country Jean Bertoin; Université Pierre et Marie Curie; France
 
3. Subject Discipline(s)
 
3. Subject Keyword(s) Lévy process; Cramér's condition; self-similar Markov process
 
3. Subject Subject classification 60G51; 60G18; 60B10
 
4. Description 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 $-\infty$ for the law of the (two-sided) path shifted at the first instant when it enters $(0,\infty)$, 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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7. Date (YYYY-MM-DD) 2011-10-31
 
8. Type Status & genre Peer-reviewed Article
 
8. Type Type
 
9. Format File format PDF
 
10. Identifier Uniform Resource Identifier http://ejp.ejpecp.org/article/view/930
 
10. Identifier Digital Object Identifier 10.1214/EJP.v16-930
 
11. Source Journal/conference title; vol., no. (year) Electronic Journal of Probability; Vol 16
 
12. Language English=en
 
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