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

Jerry Buckley, Naomi Feldheim, Eran Assaf

Research output: Contribution to journalArticlepeer-review

Abstract

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.
Original languageEnglish
Pages (from-to)999-1036
Number of pages38
JournalPROBABILITY THEORY AND RELATED FIELDS
Volume187
Issue number3-4
DOIs
Publication statusPublished - 23 Sept 2023

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