TY - JOUR

T1 - Small deviations of smooth stationary Gaussian processes

AU - Aurzada, F.

AU - Ibragimov, I. A.

AU - Lifshits, M. A.

AU - Van Zanten, J. H.

PY - 2009/12/1

Y1 - 2009/12/1

N2 - 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.

AB - 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.

KW - Gaussian processes

KW - Small deviations

KW - Spectral density

KW - Stationary processes

UR - http://www.scopus.com/inward/record.url?scp=73549112179&partnerID=8YFLogxK

U2 - 10.1137/S0040585X97983912

DO - 10.1137/S0040585X97983912

M3 - Article

AN - SCOPUS:73549112179

VL - 53

SP - 697

EP - 707

JO - Theory of Probability and its Applications

JF - Theory of Probability and its Applications

SN - 0040-585X

IS - 4

ER -