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1 results

  • Generalized Lorenz curves and convexifications of stochastic processes

  • Part of
  • Youri Davydov, Ričardas Zitikis
  • Journal:
    Journal of Applied Probability / Volume 40 / Issue 4 / September 2003
    Published online by Cambridge University Press:
    14 July 2016, pp. 906-925
    Print publication:
    September 2003

  • 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.