Seok Young Hong
Small deviations in L2-norm for Gaussian dependent sequences
Hong, Seok Young; Lifshits, Mikhail; Nazarov, Alexander
Authors
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 | 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 |
| 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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