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

被引：0

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;

D O I：

暂无

中图分类号：

学科分类号：

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.

引用

页码：999 / 1036

页数：37

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