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

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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.

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Authors and Affiliations

  1. School of Mathematics and Statistics, Carleton University, 1125 Colonel By Drive, Ottawa, ON, K1S 5B6, Canada

    Miklós Csörgő

  2. School of Mathematics and Statistics, University of Sydney, Sydney, NSW 2006, Australia

    Rafał Kulik

  3. Mathematical Institute, Wrocław University, Pl. Grunwaldzki 2/4, 50-384, Wrocław, Poland

    Rafał Kulik

Authors
  1. Miklós Csörgő
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  2. Rafał Kulik
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Corresponding author

Correspondence to Rafał Kulik.

Additional information

Research supported in part by NSERC Canada Discovery Grants of Miklós Csörgő, Donald Dawson and Barbara Szyszkowicz at Carleton University.

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Csörgő, M., Kulik, R. Weak Convergence of Vervaat and Vervaat Error Processes of Long-Range Dependent Sequences. J Theor Probab 21, 672–686 (2008). https://doi.org/10.1007/s10959-007-0124-8

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  • DOI: https://doi.org/10.1007/s10959-007-0124-8

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