Lower functions of empirical processes and brownian sheets

Research output

1 Citation (Scopus)


We give a complete characterization of the lower functions for the two-parameter Brownian sheet and for the uniform empirical process via integral criteria. Our result for the Brownian sheet can be viewed as a solution, in a very special case (the general case remains an open question), of the following problem: Find the escape rate of infinite-dimensional Brownian motion. Our result for the empirical process disproves (and provides the correct form of) a conjecture in [G. R. Shorack and J. A. Wellner, Empirical Processes with Applications to Statistics, Wiley, New York, 1986].

Original languageEnglish
Pages (from-to)273-287
Number of pages15
JournalTheory of Probability and its Applications
Issue number2
Publication statusPublished - 3 Aug 2004

Scopus subject areas

  • Statistics and Probability
  • Statistics, Probability and Uncertainty

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