Strong approximations for long memory sequences based partial sums, counting and their Vervaat processes

Endre Csáki, Miklós Csörgő, Rafał Kulik

Research output: Contribution to journalArticle

Abstract

We study the asymptotic behaviour of partial sums of long range dependent random variables and that of their counting process, together with an appropriately normalized integral process of the sum of these two processes, the so-called Vervaat process. The first two of these processes are approximated by an appropriately constructed fractional Brownian motion, while the Vervaat process in turn is approximated by the square of the same fractional Brownian motion.

Original languageEnglish
Pages (from-to)208-223
Number of pages16
JournalPeriodica Mathematica Hungarica
Volume73
Issue number2
DOIs
Publication statusPublished - Dec 1 2016

Keywords

  • Fractional Brownian motion
  • Linear process
  • Long range dependence
  • Partial sums
  • Strong approximation
  • Vervaat-type processes

ASJC Scopus subject areas

  • Mathematics(all)

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