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arXiv · 1801.10392

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
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Abstract

Let $f$ be a zero-mean continuous stationary Gaussian process on ${\mathbb R}$ whose spectral measure vanishes in a $\delta$-neighborhood of the origin. Then the probability that $f$ stays non-negative on an interval of length $L$ is at most $e^{-c\delta^2 L^2}$ with some absolute $c>0$ and the result is sharp without additional assumptions.

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Naomi Feldheim, Ohad Feldheim, Benjamin Jaye, Fedor Nazarov, Shahaf Nitzan. 2018-01-31. On the probability that a stationary Gaussian process with spectral gap remains non-negative on a long interval. https://arxiv.org/abs/1801.10392

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