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

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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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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MSC

  • 60G15
  • 60J65
  • 62J05

Keywords

  • Gaussian process
  • Small deviations
  • Precise asymptotics