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Convex rearrangements of Lévy processes

Published online by Cambridge University Press:  31 March 2007

Youri Davydov  and
Emmanuel Thilly
Youri Davydov
Affiliation:
Laboratoire Paul Painlevé - UMR 8524 université de Lille I, Bât. M2 59655, Villeneuve d'Ascq, France; youri.davydov@univ-lille1.fr
Emmanuel Thilly
Affiliation:
Laboratoire GREMARS, EA 2459 université de Lille 3, Maison de la recherche BP 149, 59653 Villeneuve d'Ascq, France; emmanuel.thilly@univ-lille3.fr
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Abstract

In this paper we study asymptotic behavior of convexrearrangements of Lévy processes. In particular weobtain Glivenko-Cantelli-type strong limit theorems for the convexifications when the corresponding Lévy measureis regularly varying at + with exponent α ∈ (1,2).

Keywords

Convex rearrangementsLévy processesstronglawsLorenz curveregularly varying functions.

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