Geodesic
Small Deviations of Smooth Stationary Gaussian Processes
Teoriâ veroâtnostej i ee primeneniâ, Tome 53 (2008) no. 4, pp. 788-798

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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.
Keywords: Gaussian processes, small deviations, spectral density, stationary processes. 
@article{TVP_2008_53_4_a8,
     author = {F. Aurzada and I. A. Ibragimov and M. A. Lifshits and H. J. van Zanden},
     title = {Small {Deviations} of {Smooth} {Stationary} {Gaussian} {Processes}},
     journal = {Teori\^a vero\^atnostej i ee primeneni\^a},
     pages = {788--798},
     publisher = {mathdoc},
     volume = {53},
     number = {4},
     year = {2008},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/TVP_2008_53_4_a8/}
}
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F. Aurzada; I. A. Ibragimov; M. A. Lifshits; H. J. van Zanden. Small Deviations of Smooth Stationary Gaussian Processes. Teoriâ veroâtnostej i ee primeneniâ, Tome 53 (2008) no. 4, pp. 788-798. http://geodesic.mathdoc.fr/item/TVP_2008_53_4_a8/