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Generalized Lorenz curves and convexifications of stochastic processes

Published online by Cambridge University Press:  14 July 2016

Youri Davydov
Affiliation:
Université des Sciences et Technologies de Lille
Ričardas Zitikis
Affiliation:
University of Western Ontario
Corresponding
E-mail address:

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.

Type
Research Papers
Copyright
Copyright © Applied Probability Trust 2003 

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