Abstract

We investigate the small deviation probabilities of a class of very smooth stationary Gaussian processes playing an important role in Bayesian statistical inference. Our calculations are based on the appropriate modification of the entropy method due to Kuelbs, Li, and Linde as well as on classical results about the entropy of classes of analytic functions. They also involve Tsirelson's upper bound for small deviations and shed some light on the limits of sharpness for that estimate.

Original languageEnglish
Pages (from-to)697-707
Number of pages11
JournalTheory of Probability and its Applications
Volume53
Issue number4
DOIs
Publication statusPublished - 1 Dec 2009

Scopus subject areas

  • Statistics and Probability
  • Statistics, Probability and Uncertainty

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