Weak convergence of Vervaat and Vervaat Error processes of long-range dependent sequences

TL;DR

This paper proves the weak convergence of Vervaat and Vervaat error processes for long-range dependent sequences, extending previous results to unbounded distributions and removing the normality assumption.

Contribution

It extends existing weak convergence results for Vervaat processes to more general distributions and dependence structures, without requiring normality.

Findings

Weak convergence of Vervaat processes established for long-range dependent sequences.

Results apply to distributions with unbounded support.

Normality assumption is no longer required.

Abstract

Following Cs\"{o}rg\H{o}, Szyszkowicz and Wang (Ann. Statist. {\bf 34}, (2006), 1013--1044) 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.