On Vervaat and Vervaat-error-type processes for partial sums and renewals

Endre Csáki, Miklós Csörgo, Zdzisław Rychlik, Josef Steinebach

Research output: Contribution to journalArticle

1 Citation (Scopus)

Abstract

We study the asymptotic behaviour of stochastic processes that are generated by sums of partial sums of i.i.d. random variables and their renewals. We conclude that these processes cannot converge weakly to any nondegenerate random element of the space D [0, 1]. On the other hand, we show that their properly normalized integrals as Vervaat-type stochastic processes converge weakly to a squared Wiener process. Moreover, we also deal with the asymptotic behaviour of the deviations of these processes, the so-called Vervaat-error-type processes.

Original languageEnglish
Pages (from-to)953-966
Number of pages14
JournalJournal of Statistical Planning and Inference
Volume137
Issue number3
DOIs
Publication statusPublished - Mar 1 2007

Keywords

  • Partial sums
  • Renewals
  • Strong and weak approximations
  • Vervaat and Vervaat-error-type processes
  • Weak convergence
  • Wiener process

ASJC Scopus subject areas

  • Statistics and Probability
  • Statistics, Probability and Uncertainty
  • Applied Mathematics

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