Journal of Theoretical Probability

, Volume 21, Issue 3, pp 672–686 | Cite as

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

Article

Abstract

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.

Keywords

Vervaat process Long range dependence 

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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

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