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Generalized Lorenz curves and convexifications of stochastic processes

  • Youri Davydov (a1) and Ričardas Zitikis (a2)

Abstract

We investigate convex rearrangements, called convexifications for brevity, of stochastic processes over fixed time intervals and develop the corresponding asymptotic theory when the time intervals indefinitely expand. In particular, we obtain strong and weak limit theorems for these convexifications when the processes are Gaussian with stationary increments and then illustrate the results using fractional Brownian motion. As a theoretical basis for these investigations, we extend some known, and also obtain new, results concerning the large sample asymptotic theory for the empirical generalized Lorenz curves and the Vervaat process when observations are stationary and either short-range or long-range dependent.

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Corresponding author

Postal address: Université des Sciences et Technologies de Lille, Laboratoire de Statistique et Probabilités, 59655 Villeneuve d'Ascq Cedex, France.
∗∗ Postal address: University of Western Ontario, Department of Statistical and Actuarial Sciences, London, Ontario N6A 5B7, Canada. Email address: zitikis@stats.uwo.ca

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Journal of Applied Probability
  • ISSN: 0021-9002
  • EISSN: 1475-6072
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