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:https://doi.org/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

Einstein Institute of Mathematics

The Hebrew University of Jerusalem

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

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

All Science Journal Classification (ASJC) codes

General Mathematics

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https://doi.org/10.1093/imrn/rny248

Cite this

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

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.",

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AU - Feldheim, Ohad

AU - Jaye, Benjamin

AU - Nazarov, Fedor

AU - Nitzan, Shahaf

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AB - 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.

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M3 - مقالة

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SP - 9210

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JO - International Mathematics Research Notices

JF - International Mathematics Research Notices

IS - 23

ER -

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

Abstract

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