Let U=(Uk) kЄℤ be a centered Gaussian stationary sequence satisfying some minor regularity condition. We study the asymptotic behavior of its weighted ℓ2-norm small deviation probabilities. It is shown that (Formula Presented) using the arguments based on the spectral theory of pseudo-differential operators by M. Birman and M. Solomyak. The constant M reflects the dependence structure of U in a non-trivial way, and marks the difference with the well-studied case of the i.i.d. sequences.

Original languageEnglish
Article number41
JournalElectronic Communications in Probability
Publication statusPublished - 1 Jan 2016

Scopus subject areas

  • Statistics and Probability
  • Statistics, Probability and Uncertainty

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