Pointwise and Uniform Asymptotics of the Vervaat Error Process

Endre Csáki (), Miklós Csörgő (), Antónia Földes (), Zhan Shi () and Ričardas Zitikis ()
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Endre Csáki: Alfréd Rényi Institute of Mathematics
Miklós Csörgő: Carleton University
Antónia Földes: City University of New York
Zhan Shi: Université Paris VI
Ričardas Zitikis: The University of Western Ontario

Journal of Theoretical Probability, 2002, vol. 15, issue 4, 845-875

Abstract: Abstract It is well known that, asymptotically, the appropriately normalized uniform Vervaat process, i.e., the integrated uniform Bahadur–Kiefer process properly normalized, behaves like the square of the uniform empirical process. We give a complete description of the strong and weak asymptotic behaviour in sup-norm of this representation of the Vervaat process and, likewise, we also study its pointwise asymptotic behaviour.

Keywords: Empirical process; quantile process; Bahadur–Kiefer process; Vervaat process; Vervaat error process; Kiefer process; Brownian bridge; Wiener process; strong approximation; law of the iterated logarithm; convergence in distribution (search for similar items in EconPapers)
Date: 2002
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Citations: View citations in EconPapers (1)

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DOI: 10.1023/A:1020650502619

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