| Issue |
ESAIM: PS
Volume 11, February 2007
Special Issue: "Stochastic analysis and mathematical finance" in honor of Nicole El Karoui's 60th birthday
|
|
|---|---|---|
| Page(s) | 161 - 172 | |
| DOI | https://doi.org/10.1051/ps:2007011 | |
| Published online | 31 March 2007 | |
Convex rearrangements of Lévy processes
1
Laboratoire Paul Painlevé - UMR 8524 université de Lille I, Bât. M2 59655, Villeneuve d'Ascq, France; youri.davydov@univ-lille1.fr
2
Laboratoire GREMARS, EA 2459 université de Lille 3, Maison de la recherche
BP 149, 59653 Villeneuve d'Ascq, France; emmanuel.thilly@univ-lille3.fr
Received:
13
March
2006
Revised:
21
June
2006
In this paper we study asymptotic behavior of convex rearrangements of Lévy processes. In particular we obtain Glivenko-Cantelli-type strong limit theorems for the convexifications when the corresponding Lévy measure is regularly varying at + with exponent α ∈ (1,2).
Mathematics Subject Classification: 60G51 / 60G52 / 60G17
Key words: Convex rearrangements / Lévy processes / strong laws / Lorenz curve / regularly varying functions.
© EDP Sciences, SMAI, 2007
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