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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… Click to show full 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.
Keywords:
probability stationary;
stationary gaussian;
gaussian process;
non negative
Journal Title: International Mathematics Research Notices
Year Published: 2018
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Journal Title: International Mathematics Research Notices
Year Published: 2018
Link to full text (if available)
Share on Social Media: Sign Up to like & get
recommendations!