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On the parabolic generator of a general one-dimensional Lévy process


 
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1. Title Title of document On the parabolic generator of a general one-dimensional Lévy process
 
2. Creator Author's name, affiliation, country Nathalie Eisenbaum; CNRS
 
2. Creator Author's name, affiliation, country Andreas Kyprianou; University of Bath
 
3. Subject Discipline(s)
 
3. Subject Keyword(s) Stochastic calculus , local time-space, It^o formula, parabolic generator.
 
3. Subject Subject classification 60G44, 60H05, 60J55, 60J65
 
4. Description Abstract The purpose of this note is twofold. Firstly to complete a recent accumulation of results concerning extended version of Ito's formula for any one dimensional Lévy processes, $X$. Secondly, we use the latter to characterise the parabolic generator of $X$, \[ {\bf A}:= \left\{ (f,g) : f(X_\cdot,\cdot) - \int_0^\cdot g(X_s, s)ds \text{ is a local martingale} \right\}. \] We also establish a necessary condition for a pair of functions to be in the domain of the parabolic generator when $X$ has a Gaussian component.
 
5. Publisher Organizing agency, location
 
6. Contributor Sponsor(s) NWO
 
7. Date (YYYY-MM-DD) 2008-04-09
 
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/1366
 
10. Identifier Digital Object Identifier 10.1214/ECP.v13-1366
 
11. Source Journal/conference title; vol., no. (year) Electronic Communications in Probability; Vol 13
 
12. Language English=en
 
14. Coverage Geo-spatial location, chronological period, research sample (gender, age, etc.)
 
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