An asymptotic formula for the variance of the number of zeroes of a stationary Gaussian process.
Fluctuations of zeroes
Gaussian process
Stationary process
Wiener Chaos
Journal
Probability theory and related fields
ISSN: 0178-8051
Titre abrégé: Probab Theory Relat Fields
Pays: Germany
ID NLM: 9881915
Informations de publication
Date de publication:
2023
2023
Historique:
received:
24
05
2022
revised:
10
05
2023
accepted:
16
06
2023
medline:
9
11
2023
pubmed:
9
11
2023
entrez:
9
11
2023
Statut:
ppublish
Résumé
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.
Identifiants
pubmed: 37941811
doi: 10.1007/s00440-023-01218-4
pii: 1218
pmc: PMC10628032
doi:
Types de publication
Journal Article
Langues
eng
Pagination
999-1036Informations de copyright
© The Author(s) 2023.