On the Probability That a Stationary Gaussian Process with Spectral Gap Remains Non-negative on a Long Interval

Naomi Feldheim; Ohad Feldheim; Benjamin Jaye; Fedor Nazarov; Shahaf Nitzan

doi:10.1093/imrn/rny248

On the Probability That a Stationary Gaussian Process with Spectral Gap Remains Non-negative on a Long Interval

Naomi Feldheim^*, Ohad Feldheim, Benjamin Jaye, Fedor Nazarov, Shahaf Nitzan

^*Corresponding author for this work

Einstein Institute of Mathematics

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

1 Scopus citations

Abstract

Let f be a zero mean continuous stationary Gaussian process on ℝ whose spectral measure vanishes in a δ-neighborhood of the origin. Then, the probability that f stays non-negative on an interval of length L is at most e-cδ2L2 with some absolute c > 0 and the result is sharp without additional assumptions.

Original language	English
Pages (from-to)	9210-9227
Number of pages	18
Journal	International Mathematics Research Notices
Volume	2020
Issue number	23
DOIs	https://doi.org/10.1093/imrn/rny248
State	Published - 1 Nov 2020

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© 2018 The Author(s). Published by Oxford University Press. All rights reserved.

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On the Probability That a Stationary Gaussian Process with Spectral Gap Remains Non-negative on a Long Interval

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