Journal of Theoretical Probability

, Volume 21, Issue 3, pp 672-686

First online:

Weak Convergence of Vervaat and Vervaat Error Processes of Long-Range Dependent Sequences

  • Miklós CsörgőAffiliated withSchool of Mathematics and Statistics, Carleton University
  • , Rafał KulikAffiliated withSchool of Mathematics and Statistics, University of SydneyMathematical Institute, Wrocław University Email author 

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Following Csörgő, Szyszkowicz and Wang (Ann. Stat. 34, 1013–1044, 2006) we consider a long range dependent linear sequence. We prove weak convergence of the uniform Vervaat and the uniform Vervaat error processes, extending their results to distributions with unbounded support and removing normality assumption.


Vervaat process Long range dependence