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

Research output: Contribution to journalArticlepeer-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 languageAmerican English
Pages (from-to)9210-9227
Number of pages18
JournalInternational Mathematics Research Notices
Volume2020
Issue number23
DOIs
StatePublished - 1 Nov 2020

Bibliographical note

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

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