ESAIM: Probability and Statistics

Table of Contents - August 2007 - Volume 11, Special Issue: "Stochastic analysis and mathematical finance" in honor of Nicole El Karoui's 60th birthday  

Research Article

Convex rearrangements of Lévy processes

Davydov, Youria1 and Thilly, Emmanuela2

a1 Laboratoire Paul Painlevé - UMR 8524 université de Lille I, Bât. M2 59655, Villeneuve d'Ascq, France; youri.davydov@univ-lille1.fr

a2 Laboratoire GREMARS, EA 2459 université de Lille 3, Maison de la recherche BP 149, 59653 Villeneuve d'Ascq, France; emmanuel.thilly@univ-lille3.fr

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).

(Received March 13 2006)

(Revised June 21 2006)

(Online publication March 31 2007)

Key Words:

  • Convex rearrangements;
  • Lévy processes;
  • strong laws;
  • Lorenz curve;
  • regularly varying functions.

Mathematics Subject Classification:

  • 60G51;
  • 60G52;
  • 60G17
--