Skip to main content

Research Repository

Advanced Search

Small deviations in L2-norm for Gaussian dependent sequences

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


Seok Young Hong

Mikhail Lifshits

Alexander Nazarov


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.


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 Oct 22, 2018
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
Public URL
Publisher URL
Related Public URLs


Downloadable Citations