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An optimal Itô formula for Lévy processes


 
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1. Title Title of document An optimal Itô formula for Lévy processes
 
2. Creator Author's name, affiliation, country Nathalie Eisenbaum; LPMA, Université Paris 6
 
2. Creator Author's name, affiliation, country Alexander Walsh; LPMA, Université Paris 6
 
3. Subject Discipline(s)
 
3. Subject Keyword(s) stochastic calculus, Lévy process, local time, Itô formula
 
3. Subject Subject classification 60G44, 60H05, 60J55, 60J65
 
4. Description Abstract Several Itô formulas have been already established for Lévy processes. We explain according to which criteria they are not optimal and establish an extended Itô formula that satisfies that criteria. The interest, in particular, of this formula is to obtain the explicit decomposition of $F(X)$, for $X$ Lévy process and $F$ deterministic function with locally bounded first order Radon-Nikodym derivatives, as the sum of a Dirichlet process and a bounded variation process.
 
5. Publisher Organizing agency, location
 
6. Contributor Sponsor(s)
 
7. Date (YYYY-MM-DD) 2009-04-24
 
8. Type Status & genre Peer-reviewed Article
 
8. Type Type
 
9. Format File format PDF
 
10. Identifier Uniform Resource Identifier http://ecp.ejpecp.org/article/view/1469
 
10. Identifier Digital Object Identifier 10.1214/ECP.v14-1469
 
11. Source Journal/conference title; vol., no. (year) Electronic Communications in Probability; Vol 14
 
12. Language English=en
 
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