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Small deviations in L2-norm for Gaussian dependent sequences
University of Cambridge, UK.
Linköping University, Department of Mathematics. Linköping University, Faculty of Science & Engineering. St.Petersburg State University, Russia.
St.Petersburg State University, Russia.
2016 (English)In: Electronic Communications in Probability, ISSN 1083-589X, E-ISSN 1083-589X, ., Vol. 21, no 41Article in journal (Refereed) PublishedText
Abstract [en]

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.

Place, publisher, year, edition, pages
Keyword [en]
Small deviations; spectral asymptotics; stationary sequences
National Category
Probability Theory and Statistics
URN: urn:nbn:se:liu:diva-128660DOI: 10.1214/16-ECP4708ISI: 000378990200040OAI: diva2:931240

Funding agencies: ERC grant AdG-NAMSEF; RFBR grant [16-01-00258]

Available from: 2016-05-27 Created: 2016-05-27 Last updated: 2016-08-06Bibliographically approved

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Lifshits, Mikhail
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