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

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 spe...

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Autores principales: Assaf, Eran, Buckley, Jeremiah, Feldheim, Naomi
Formato: Online Artículo Texto
Lenguaje:English
Publicado: Springer Berlin Heidelberg 2023
Materias:
Article
Acceso en línea:https://www.ncbi.nlm.nih.gov/pmc/articles/PMC10628032/
https://www.ncbi.nlm.nih.gov/pubmed/37941811
http://dx.doi.org/10.1007/s00440-023-01218-4
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author Assaf, Eran
Buckley, Jeremiah
Feldheim, Naomi
author_facet Assaf, Eran
Buckley, Jeremiah
Feldheim, Naomi
author_sort Assaf, Eran
collection PubMed
description 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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spelling pubmed-106280322023-11-08 An asymptotic formula for the variance of the number of zeroes of a stationary Gaussian process Assaf, Eran Buckley, Jeremiah Feldheim, Naomi Probab Theory Relat Fields Article 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. Springer Berlin Heidelberg 2023-09-23 2023 /pmc/articles/PMC10628032/ /pubmed/37941811 http://dx.doi.org/10.1007/s00440-023-01218-4 Text en © The Author(s) 2023 https://creativecommons.org/licenses/by/4.0/Open Access This article is licensed under a Creative Commons Attribution 4.0 International License, which permits use, sharing, adaptation, distribution and reproduction in any medium or format, as long as you give appropriate credit to the original author(s) and the source, provide a link to the Creative Commons licence, and indicate if changes were made. The images or other third party material in this article are included in the article’s Creative Commons licence, unless indicated otherwise in a credit line to the material. If material is not included in the article’s Creative Commons licence and your intended use is not permitted by statutory regulation or exceeds the permitted use, you will need to obtain permission directly from the copyright holder. To view a copy of this licence, visit http://creativecommons.org/licenses/by/4.0/ (https://creativecommons.org/licenses/by/4.0/) .
spellingShingle Article
Assaf, Eran
Buckley, Jeremiah
Feldheim, Naomi
An asymptotic formula for the variance of the number of zeroes of a stationary Gaussian process
title An asymptotic formula for the variance of the number of zeroes of a stationary Gaussian process
title_full An asymptotic formula for the variance of the number of zeroes of a stationary Gaussian process
title_fullStr An asymptotic formula for the variance of the number of zeroes of a stationary Gaussian process
title_full_unstemmed An asymptotic formula for the variance of the number of zeroes of a stationary Gaussian process
title_short An asymptotic formula for the variance of the number of zeroes of a stationary Gaussian process
title_sort asymptotic formula for the variance of the number of zeroes of a stationary gaussian process
topic Article
url https://www.ncbi.nlm.nih.gov/pmc/articles/PMC10628032/
https://www.ncbi.nlm.nih.gov/pubmed/37941811
http://dx.doi.org/10.1007/s00440-023-01218-4
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