MWI representation of the number of curve-crossings by a differentiable Gaussian process, with applications

DOI10.1214/aop/1176988606zbMath0819.60036OpenAlexW2056430354MaRDI QIDQ1345603

Eric V. Slud

Publication date: 15 August 1995

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

Full work available at URL: https://doi.org/10.1214/aop/1176988606

zbMATH Keywords

multiple Wiener integralRice's formulacentral and noncentral limit theorems

Mathematics Subject Classification ID

Gaussian processes (60G15) Central limit and other weak theorems (60F05) Signal detection and filtering (aspects of stochastic processes) (60G35)

Related Items

The winding of stationary Gaussian processes ⋮ Fluctuations of the number of excursion sets of planar Gaussian fields ⋮ A CLT concerning critical points of random functions on a Euclidean space ⋮ Hermite polynomial expansion for non-smooth functionals of stationary Gaussian processes: Crossings and extremes ⋮ 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 ⋮ Winding number for stationary Gaussian processes using real variables ⋮ Gaussian complex zeroes are not always normal: limit theorems on the disc ⋮ Level curves crossings and applications for Gaussian models ⋮ Central limit theorem for Lipschitz-Killing curvatures of excursion sets of Gaussian random fields ⋮ Estimation of local anisotropy based on level sets ⋮ Variance estimator for fractional diffusions with variance and drift depending on time