On the second moment of the number of crossings by a stationary Gaussian process

DOI10.1214/009117906000000142zbMath1101.60024arXivmath/0609682OpenAlexW3101411295MaRDI QIDQ850983

Marie F. Kratz, José Rafael León

Publication date: 8 November 2006

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

Full work available at URL: https://arxiv.org/abs/math/0609682

Mathematics Subject Classification ID

Gaussian processes (60G15) Stationary stochastic processes (60G10) Extreme value theory; extremal stochastic processes (60G70)

Related Items (8)

Number of critical points of a Gaussian random field: condition for a finite variance ⋮ On the second moment of the number of crossings by a stationary Gaussian process ⋮ A second moment bound for critical points of planar Gaussian fields in shrinking height windows ⋮ An asymptotic formula for the variance of the number of zeroes of a stationary Gaussian process ⋮ On the finiteness of the moments of the measure of level sets of random fields ⋮ Necessary and sufficient conditions for the finiteness of the second moment of the measure of level sets ⋮ Level curves crossings and applications for Gaussian models ⋮ Central limit theorem for Lipschitz-Killing curvatures of excursion sets of Gaussian random fields

Cites Work

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• On the second moment of the number of crossings by a stationary Gaussian process
• Correction to: Local nondeterminism and the zeros of Gaussian processes
• Conditions for finite moments of the number of zero crossings for Gaussian processes
• Local nondeterminism and the zeros of Gaussian processes
• The expected number of zeros of continuous stationary Gaussian processes
• Law of the iterated logarithm for sums of non-linear functions of Gaussian variables that exhibit a long range dependence
• The Expected Number of Zeros of a Stationary Gaussian Process
• On a Theorem of Cramer and Leadbetter
• On the Variance of the Number of Zeros of a Stationary Gaussian Process
• Mathematical Analysis of Random Noise

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