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

In: Electronic Communications in Probability, Vol. 21, 41, 01.01.2016.

Research output: Contribution to journal › Article › peer-review

Harvard

Hong, SY, Lifshits, M & Nazarov, A 2016, 'Small deviations in L2-norm for Gaussian dependent sequences', Electronic Communications in Probability, vol. 21, 41. https://doi.org/10.1214/16-ECP4708

APA

Hong, S. Y., Lifshits, M., & Nazarov, A. (2016). Small deviations in L2-norm for Gaussian dependent sequences. Electronic Communications in Probability, 21, [41]. https://doi.org/10.1214/16-ECP4708

Vancouver

Hong SY, Lifshits M, Nazarov A. Small deviations in L2-norm for Gaussian dependent sequences. Electronic Communications in Probability. 2016 Jan 1;21. 41. https://doi.org/10.1214/16-ECP4708

Author

Hong, Seok Young ; Lifshits, Mikhail ; Nazarov, Alexander. / Small deviations in L2-norm for Gaussian dependent sequences. In: Electronic Communications in Probability. 2016 ; Vol. 21.

BibTeX

@article{66f291766c3647ff9cc16999c46c361f,
title = "Small deviations in L2-norm for Gaussian dependent sequences",
abstract = "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.",
keywords = "Small deviations, Spectral asymptotics, Stationary sequences",
author = "Hong, {Seok Young} and Mikhail Lifshits and Alexander Nazarov",
year = "2016",
month = jan,
day = "1",
doi = "10.1214/16-ECP4708",
language = "English",
volume = "21",
journal = "Electronic Communications in Probability",
issn = "1083-589X",
publisher = "Institute of Mathematical Statistics",

}

RIS

TY - JOUR

T1 - Small deviations in L2-norm for Gaussian dependent sequences

AU - Hong, Seok Young

AU - Lifshits, Mikhail

AU - Nazarov, Alexander

PY - 2016/1/1

Y1 - 2016/1/1

N2 - 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.

AB - 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.

KW - Small deviations

KW - Spectral asymptotics

KW - Stationary sequences

UR - http://www.scopus.com/inward/record.url?scp=84973860866&partnerID=8YFLogxK

U2 - 10.1214/16-ECP4708

DO - 10.1214/16-ECP4708

M3 - Article

AN - SCOPUS:84973860866

VL - 21

JO - Electronic Communications in Probability

JF - Electronic Communications in Probability

SN - 1083-589X

M1 - 41

ER -

ID: 45778213