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Small deviations in L2-norm for Gaussian dependent sequences

Hong, Seok Young; Lifshits, Mikhail; Nazarov, Alexander

Authors

Seok Young Hong

Mikhail Lifshits

Alexander Nazarov



Abstract

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.

Citation

Young Hong, S., Lifshits, M., & Nazarov, A. (2016). Small deviations in L2-norm for Gaussian dependent sequences. Electronic Communications in Probability, 21(41), (1-9). doi:10.1214/16-ECP4708. ISSN 1083-589X

Journal Article Type Article
Acceptance Date May 10, 2016
Online Publication Date May 27, 2016
Publication Date May 27, 2016
Deposit Date Oct 22, 2018
Publicly Available Date Mar 29, 2024
Journal Electronic Communications in Probablity
Electronic ISSN 1083-589X
Publisher Institute of Mathematical Statistics (IMS)
Peer Reviewed Peer Reviewed
Volume 21
Issue 41
Pages 1-9
DOI https://doi.org/10.1214/16-ECP4708
Public URL https://nottingham-repository.worktribe.com/output/1178789
Publisher URL https://projecteuclid.org/euclid.ecp/1463663122
Related Public URLs https://projecteuclid.org/euclid.ecp/1463663122

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