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 special frequency does not affect the asymptotic growth of the variance, while an atom at any other frequency results in maximal growth. Our results allow us to analyse a large number of interesting examples.
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Probability
Classical Analysis and ODEs
60G10, 60G15 (Primary) 05A19, 37A46, 42A38 (Secondary)
