未找到相关数据
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
收藏
页码：999 / 1036
页数：37
相关论文
未找到相关数据