Journal of Theoretical Probability

, Volume 21, Issue 3, pp 672–686

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


DOI: 10.1007/s10959-007-0124-8

Cite this article as:
Csörgő, M. & Kulik, R. J Theor Probab (2008) 21: 672. doi:10.1007/s10959-007-0124-8


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 processLong range dependence

Copyright information

© Springer Science+Business Media, LLC 2007

Authors and Affiliations

  1. 1.School of Mathematics and StatisticsCarleton UniversityOttawaCanada
  2. 2.School of Mathematics and StatisticsUniversity of SydneySydneyAustralia
  3. 3.Mathematical InstituteWrocław UniversityWrocławPoland