Small deviations in $L_2$-norm for Gaussian dependent sequences

Let be a centered Gaussian stationary sequence satisfying some minor regularity condition. We study the asymptotic behavior of its weighted -norm small deviation probabilities. It is shown that whenever using the arguments based on the spectral theory of pseudo-differential operators by M. Birman an...

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Bibliographic Details
Published inElectronic communications in probability Vol. 21; no. none
Main Authors Hong, Seok Young, Lifshits, Mikhail, Nazarov, Alexander
Format Journal Article
LanguageEnglish
Published 01.01.2016
Subjects
Small deviations
spectral asymptotics
stationary sequences
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Summary:Let be a centered Gaussian stationary sequence satisfying some minor regularity condition. We study the asymptotic behavior of its weighted -norm small deviation probabilities. It is shown that whenever using the arguments based on the spectral theory of pseudo-differential operators by M. Birman and M. Solomyak. The constant reflects the dependence structure of in a non-trivial way, and marks the difference with the well-studied case of the i.i.d. sequences.
ISSN:1083-589X
1083-589X
DOI:10.1214/16-ECP4708