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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 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).

Keywords

Convex rearrangementsLévy processesstrong lawsLorenz curveregularly varying functions.
Type
Research Article
Information
ESAIM: Probability and Statistics , Volume 11: Special Issue: "Stochastic analysis and mathematical finance" in honor of Nicole El Karoui's 60th birthdaySpecial Issue: "Stochastic analysis and mathematical finance" in honor of Nicole El Karoui's 60th birthday , June 2007 , pp. 161 - 172
Copyright
© EDP Sciences, SMAI, 2007

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