ESAIM: P&S, March 2007, Vol. 11, pp. 161-172
DOI: 10.1051/ps:2007011

Convex rearrangements of Lévy processes

Youri Davydov¹ and Emmanuel Thilly<sup>2

1</sup>  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 March 13, 2006. Revised June 21, 2006. Published online 31 March 2007.)

Abstract
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 0⁺ with exponent .

Mathematics Subject Classification. 60G51, 60G52, 60G17.

Key words: Convex rearrangements, Lévy processes, strong laws, Lorenz curve, regularly varying functions.


© EDP Sciences, SMAI 2007