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 ${\mathbb R}$ 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.
- Publication:
-
arXiv e-prints
- Pub Date:
- January 2018
- DOI:
- 10.48550/arXiv.1801.10392
- arXiv:
- arXiv:1801.10392
- Bibcode:
- 2018arXiv180110392F
- Keywords:
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- Mathematics - Probability;
- Mathematical Physics;
- Mathematics - Classical Analysis and ODEs;
- 60G10;
- 60G15
- E-Print:
- 15 pages. To appear in IMRN (Inter. Math. Res. Notices)