English

$L_2$-Small Deviations for Weighted Stationary Processes

Probability 2020-02-11 v2

Abstract

We find logarithmic asymptotics of L2L_2-small deviation probabilities for weighted stationary Gaussian processes (both for real and complex-valued) having power-type discrete or continuous spectrum. As in the recent work by Hong, Lifshits and Nazarov, our results are based on the spectral theory of pseudo-differential operators developed by Birman and Solomyak.

Keywords

Cite

@article{arxiv.1705.00422,
  title  = {$L_2$-Small Deviations for Weighted Stationary Processes},
  author = {Mikhail Lifshits and Alexander Nazarov},
  journal= {arXiv preprint arXiv:1705.00422},
  year   = {2020}
}
R2 v1 2026-06-22T19:32:30.610Z