An asymptotic formula for the variance of the number of zeroes of a stationary Gaussian process

被引:0
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作者
Eran Assaf
Jeremiah Buckley
Naomi Feldheim
机构
[1] Dartmouth College,
[2] King’s College,undefined
[3] Bar-Ilan University,undefined
来源
Probability Theory and Related Fields | 2023年 / 187卷
关键词
Gaussian process; Stationary process; Fluctuations of zeroes; Wiener Chaos; Primary: 60G10; 60G15; Secondary: 05A19; 37A46; 42A38;
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摘要
We study the variance of the number of zeroes of a stationary Gaussian process on a long interval. We give a simple asymptotic description under mild mixing conditions. This allows us to characterise minimal and maximal growth. We show that a small (symmetrised) atom in the spectral measure at a special frequency does not affect the asymptotic growth of the variance, while an atom at any other frequency results in maximal growth.
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页码:999 / 1036
页数:37
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