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

• 成果类型: Article
• 署名作者: Assaf, Eran; Buckley, Jeremiah; Feldheim, Naomi
• 署名单位: Dartmouth College; University of London; King's College London; Bar Ilan University
• 刊物名称: PROBABILITY THEORY AND RELATED FIELDS
• ISSN/ISSBN: 0178-8051
• DOI: 10.1007/s00440-023-01218-4
• 发表日期: 2023
• 页码: 999-1036
• 关键词: crossings

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.