Some liminf results for two-parameter processes

Endre Csáki, Zhan Shi

Research output: Contribution to journalArticle

2 Citations (Scopus)


We obtain some liminf limits for the Wiener sheet. The approach relies on a careful analysis of the lower tail of the Ornstein-Uhlenbeck process. Our results can be applied to normalized Kiefer and empirical processes. In particular, they yield a satisfying answer to Hirsch's problem for the uniform empirical distribution function.

Original languageEnglish
Pages (from-to)27-46
Number of pages20
JournalStochastic Processes and their Applications
Issue number1
Publication statusPublished - Oct 1 1998


  • 60F15
  • 60J65
  • Empirical process
  • Kiefer process
  • Ornstein-Uhlenbeck process
  • Wiener sheet

ASJC Scopus subject areas

  • Statistics and Probability
  • Modelling and Simulation
  • Applied Mathematics

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