Asymptotics for the local time of a strongly dependent vector-valued Gaussian random field

DOI10.1007/BF02187395zbMath0874.60046OpenAlexW1985814741MaRDI QIDQ1912701

Paul Doukhan, José Rafael León

Publication date: 10 November 1997

Published in: Acta Mathematica Hungarica (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1007/bf02187395

zbMATH Keywords

asymptotic behaviourHermite polynomialsstationarylocal timelong range dependenceEdgeworth expansionGaussian random fieldsrandom spectral measures

Mathematics Subject Classification ID

Random fields (60G60) Central limit and other weak theorems (60F05)

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Cites Work

• On smoothed probability density estimation for stationary processes
• Multiple stochastic integrals with dependent integrators
• Local times of stochastic processes with positive definite bivariate densities
• Occupation densities
• Non-central limit theorems for non-linear functionals of \(k\) Gaussian fields
• Necessary conditions for nonlinear functionals of Gaussian processes to satisfy central limit theorems
• Functional estimation for time series. I: Quadratic convergence properties
• Local Times for Multiparameter Random Processes
• On Sojourn Times for Functions and Random Processes
• Law of the iterated logarithm for sums of non-linear functions of Gaussian variables that exhibit a long range dependence
• Non-central limit theorems for non-linear functional of Gaussian fields
• On Local Times for Random Processes
• Local Times and Sample Function Properties of Stationary Gaussian Processes