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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...
| Autores principales: | , , |
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| Formato: | Online Artículo Texto |
| Lenguaje: | English |
| Publicado: |
Springer Berlin Heidelberg
2023
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| Materias: | |
| 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 |
| Sumario: | 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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