A central limit theorem for the number of zeros of a stationary Gaussian process

DOI10.1214/aop/1176996026zbMath0348.60048OpenAlexW2027748205MaRDI QIDQ1234528

Jack Cuzick

Publication date: 1976

Published in: The Annals of Probability (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1214/aop/1176996026

Mathematics Subject Classification ID

Gaussian processes (60G15) Central limit and other weak theorems (60F05) Sample path properties (60G17)

Related Items

Variance of the number of zeroes of shift-invariant Gaussian analytic functions ⋮ The winding of stationary Gaussian processes ⋮ A central limit theorem for non-instantaneous filters of a stationary Gaussian process ⋮ A CLT concerning critical points of random functions on a Euclidean space ⋮ The sharp phase transition for level set percolation of smooth planar Gaussian fields ⋮ Limit Theorems for Excursion Sets of Stationary Random Fields ⋮ Asymptotic theory for curve-crossing analysis ⋮ Asymptotic normality of high level-large time crossings of a Gaussian process ⋮ An asymptotic formula for the variance of the number of zeroes of a stationary Gaussian process ⋮ Cumulants asymptotics for the zeros counting measure of real Gaussian processes ⋮ A sprinkled decoupling inequality for Gaussian processes and applications ⋮ Gaussian complex zeroes are not always normal: limit theorems on the disc ⋮ Rice formulae and Gaussian waves ⋮ Multiple Wiener-Itô integral expansions for level-crossing-count functionals ⋮ Spectral conditions for sojourn and extreme value limit theorems for Gaussian processes ⋮ Zeros of smooth stationary Gaussian processes ⋮ Necessary conditions for nonlinear functionals of Gaussian processes to satisfy central limit theorems ⋮ On excursion sets, tube formulas and maxima of random fields. ⋮ Diophantine Gaussian excursions and random walks ⋮ Variance linearity for real Gaussian zeros

This page was built for publication: A central limit theorem for the number of zeros of a stationary Gaussian process