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Precise small deviations in L 2 of some Gaussian processes appearing in the regression context

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Central European Journal of Mathematics

Abstract

We find precise small deviation asymptotics with respect to the Hilbert norm for some special Gaussian processes connected to two regression schemes studied by MacNeill and his coauthors. In addition, we also obtain precise small deviation asymptotics for the detrended Brownian motion and detrended Slepian process.

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Authors and Affiliations

  1. Korteweg-de Vries Institute for Mathematics, University of Amsterdam, P. O. Box 19268, 1000 GG, Amsterdam, The Netherlands

    Alisa A. Kirichenko

  2. Department of Mathematics and Mechanics, Saint-Petersburg State University, Universitetski pr., 28, St. Petersburg, 198504, Russia

    Ya. Yu. Nikitin

  3. National Research University — Higher School of Economics, Souza Pechatnikov, 16, St. Petersburg, 190008, Russia

    Ya. Yu. Nikitin

Authors
  1. Alisa A. Kirichenko
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  2. Ya. Yu. Nikitin
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Correspondence to Alisa A. Kirichenko.

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Kirichenko, A.A., Nikitin, Y.Y. Precise small deviations in L 2 of some Gaussian processes appearing in the regression context. centr.eur.j.math. 12, 1674–1686 (2014). https://doi.org/10.2478/s11533-014-0436-8

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  • DOI: https://doi.org/10.2478/s11533-014-0436-8

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