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

Author

Listed:
  • Miklós Csörgő

    (Carleton University)

  • Rafał Kulik

    (University of Sydney
    Wrocław University)

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.

Suggested Citation

  • Miklós Csörgő & Rafał Kulik, 2008. "Weak Convergence of Vervaat and Vervaat Error Processes of Long-Range Dependent Sequences," Journal of Theoretical Probability, Springer, vol. 21(3), pages 672-686, September.
    • Handle: RePEc:spr:jotpro:v:21:y:2008:i:3:d:10.1007_s10959-007-0124-8
    DOI: 10.1007/s10959-007-0124-8
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    References listed on IDEAS

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    1. Tailen Hsing, 2000. "Linear Processes, Long-Range Dependence and Asymptotic Expansions," Statistical Inference for Stochastic Processes, Springer, vol. 3(1), pages 19-29, January.
    2. Endre Csáki & Miklós Csörgő & Antónia Földes & Zhan Shi & Ričardas Zitikis, 2002. "Pointwise and Uniform Asymptotics of the Vervaat Error Process," Journal of Theoretical Probability, Springer, vol. 15(4), pages 845-875, October.
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    Keywords

    Vervaat process; Long range dependence;

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