Large deviations application to Billingsley's example

Robert Liptser*

*Corresponding author for this work

Research output: Contribution to journalArticlepeer-review


We consider a classical model related to an empirical distribution function sequence of random variables, supported on the interval [0,1], with continuous distribution function F(t) = P(ξ1 ≤ t). Applying "Stopping Time Techniques", we give a proof of Kolmogorov's exponential bound conjectured by Kolmogorov in 1943. Using this bound we establish a best possible logarithmic asymptotic of with rate slower than 1/n for any α ε (0,1/2).

Original languageEnglish
Pages (from-to)263-274
Number of pages12
JournalSequential Analysis
Issue number3
StatePublished - 2010


  • Empirical distribution
  • Large deviations principle
  • Stopping time


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