Universiteit Utrecht

Department of Mathematics

Small deviations of smooth stationary Gaussian processes

Harry van Zanten (VU)
14 May 2008

We investigate the small deviation probabilities of a class of very smooth stationary Gaussian processes playing an important role in nonparametric Bayesian statistics. Our calculations are based on an 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. The talk is based on joint work with F.Aurzada, I.A.Ibragimov and M.A.Lifshits. See http://arxiv.org/abs/0803.4238

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