"Pointwise and uniform asymptotics of the Vervaat error process"

Endre Csáki, Miklós Csörgö, Antónia Földes, Zhan Shi and Ricardas Zitikis

Summary: 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 study also its pointwise asymptotic behaviour.

Keywords: Empirical process, quantile process, Bahadur-Kiefer process, Vervaat process.

2000 Mathematics Subject Classification: Primary 60F15; Secondary 60F05, 60F17.