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Teoriya Veroyatnostei i ee Primeneniya, 2008, Volume 53, Issue 4, Pages 788–798
DOI: https://doi.org/10.4213/tvp2466 (Mi tvp2466) 		 
This article is cited in 16 scientific papers (total in 16 papers)

Short Communications

Small Deviations of Smooth Stationary Gaussian Processes

F. Aurzadaa, I. A. Ibragimovb, M. A. Lifshitsb, H. J. van Zandenc

a University of Sciences and Technologies
b Saint-Petersburg State University
c Vrije Universiteit Amsterdam
Full-text PDF (1262 kB) Citations (16)
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DOI: https://doi.org/10.4213/tvp2466
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.
Keywords: Gaussian processes, small deviations, spectral density, stationary processes.
Received: 29.03.2008
English version:
Theory of Probability and its Applications, 2009, Volume 53, Issue 4, Pages 697–707
DOI: https://doi.org/10.1137/S0040585X97983912
Bibliographic databases:
Document Type: Article
Language: Russian
Citation: F. Aurzada, I. A. Ibragimov, M. A. Lifshits, H. J. van Zanden, “Small Deviations of Smooth Stationary Gaussian Processes”, Teor. Veroyatnost. i Primenen., 53:4 (2008), 788–798; Theory Probab. Appl., 53:4 (2009), 697–707
Citation in format AMSBIB
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    • This publication is cited in the following 16 articles:
    Citing articles in Google Scholar: Russian citations, English citations
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    		Теория вероятностей и ее применения Theory of Probability and its Applications
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