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Central Limit Theorems for Level Functionals of Stationary Gaussian Processes and Fields
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What this work says
Outgoing claims: the papers this work cites, builds on, or argues with.
inferredcites →https://doi.org/10.1007/978-1-4615-8162-8_1openalex-snapshot
On Central and Non-Central Limit Theorems for Non-Linear Functions of a Stationary Gaussian Process
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Law of the iterated logarithm for sums of non-linear functions of Gaussian variables that exhibit a long range dependence
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Approximation du temps local des surfaces gaussiennes
inferredcites →https://doi.org/10.1007/bf01312215openalex-snapshot
Multiple Wiener-itô integral expansions for level-crossing-count functionals
inferredcites →https://doi.org/10.1007/bf02451428openalex-snapshot
CLT and other limit theorems for functionals of Gaussian processes
inferredcites →https://doi.org/10.1016/0047-259x(83)90019-2openalex-snapshot
Central limit theorems for non-linear functionals of Gaussian fields
inferredcites →https://doi.org/10.1016/0304-4149(94)00041-qopenalex-snapshot
Chaos expansions of double intersection local time of Brownian motion in Rd and renormalization
inferredcites →https://doi.org/10.1016/s0304-4149(96)00122-6openalex-snapshot
Hermite polynomial expansion for non-smooth functionals of stationary Gaussian processes: Crossings and extremes
inferredcites →https://doi.org/10.1023/a:1009975204538openalex-snapshot
Central Limit Theorems for the Number of Maxima and an Estimator of the Second Spectral Moment of a Stationary Gaussian Process, with Application to Hydroscience
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The Geometry of Random Fields
inferredcites →https://doi.org/10.1137/1114035openalex-snapshot
Asymptotic Normality of the Number of Crossings of Level Zero by a Gaussian Process
inferredcites →https://doi.org/10.1214/aoms/1177692560openalex-snapshot
On the Variance of the Number of Zeros of a Stationary Gaussian Process
inferredcites →https://doi.org/10.1214/aop/1176988503openalex-snapshot
Limit Theorems for Nonlinear Functionals of a Stationary Gaussian Sequence of Vectors
inferredcites →https://doi.org/10.1214/aop/1176988606openalex-snapshot
MWI Representation of the Number of Curve-Crossings by a Differentiable Gaussian Process, with Applications
inferredcites →https://doi.org/10.1214/aop/1176989918openalex-snapshot
A Central Limit Theorem for the Renormalized Self-Intersection Local Time of a Stationary Vector Gaussian Process
inferredcites →https://doi.org/10.1214/aop/1176996026openalex-snapshot
A Central Limit Theorem for the Number of Zeros of a Stationary Gaussian Process
inferredcites →https://doi.org/10.1215/s0012-7094-48-01568-3openalex-snapshot
The central limit theorem for dependent random variables
What points at this work
Incoming claims: where this work appears in other papers’ reference lists and arguments.
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Quantitative Breuer-Major Theorems
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On the Capacity Functional of Excursion Sets of Gaussian Random Fields on R²
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CLT for Lipschitz-Killing Curvatures of Excursion Sets of Gaussian Random Fields
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References and Suggested Reading
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Gaussian Fields Through Geometrical Properties
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Hermite Expansions of Level Functionals
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Limit Theorems for Excursion Sets of Stationary Random Fields
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Central Limit Theorems for Weakly Dependent Random Fields
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Asymptotic Methods for Random Tessellations
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Non-Universality of Nodal Length Distribution for Arithmetic Random Waves
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Boundary Effect on the Nodal Length for Arithmetic Random Waves, and Spectral Semi-correlations
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Level curves crossings and applications for Gaussian models
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High-Level Moving Excursions for Spatiotemporal Gaussian Random Fields with Long Range Dependence
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Central Limit Theorem for Lipschitz–Killing Curvatures of Excursion Sets of Gaussian Random Fields
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A sharp transition in zero overcrowding and undercrowding probabilities for stationary Gaussian processes
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Limit Theorems for the Number of Up-crossings of the Conjunction Set of Stationary Gaussian Processes
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On the nodal structures of random fields: a decade of results
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Asymptotic variance and CLT for the number of zeros of Kostlan Shub Smale random polynomials
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A central limit theorem for Lipschitz–Killing curvatures of Gaussian excursions
inferred← citeshttps://doi.org/10.1016/j.spa.2010.12.006openalex-snapshot
Quantitative Breuer–Major theorems
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On the rate of convergence for central limit theorems of sojourn times of Gaussian fields
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A central limit theorem for the Euler integral of a Gaussian random field
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A CLT concerning critical points of random functions on a Euclidean space
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Asymptotic normality of high level-large time crossings of a Gaussian process
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Asymptotic behaviour of level sets of needlet random fields
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The spatial sojourn time for the solution to the wave equation with moving time: Central and non-central limit theorems
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A functional central limit theorem for the level measure of a Gaussian random field
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On the capacity functional of excursion sets of Gaussian random fields on ℝ2
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Rates for the SLLN for long-memory and heavy-tailed processes
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Geometrical characteristics of Gaussian sea waves
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Asymptotic distribution of nodal intersections for ARW against a surface
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Variance of the volume of random real algebraic submanifolds
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Nodal area distribution for arithmetic random waves
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Nodal volumes as differentiable functionals of Gaussian fields
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Overcrowding Estimates for the Nodal Volume of Stationary Gaussian Processes
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On the perimeter estimation of pixelated excursion sets of two‐dimensional anisotropic random fields
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Functional Central Limit Theorem for the Measures of Level Surfaces of the Gaussian Random Field
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Cross-Correlations and Joint Gaussianity in Multivariate Level Crossing Models
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A central limit theorem for the Euler characteristic of a Gaussian excursion set
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Level crossings and other level functionals of stationary Gaussian processes
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The asymptotic equivalence of the sample trispectrum and the nodal length for random spherical harmonics
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Necessary and sufficient conditions for the finiteness of the second moment of the measure of level sets
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Variance linearity for real Gaussian zeros
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Estimation of local anisotropy based on level sets
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Winding number for stationary Gaussian processes using real variables
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A covariance formula for the number of excursion set components of Gaussian fields and applications
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The phase transition for planar Gaussian percolation models without FKG
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A central limit theorem for the number of excursion set components of Gaussian fields
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On a general Kac–Rice formula for the measure of a level set
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The anisotropy of 2D or 3D Gaussian random fields through their Lipschitz–Killing curvature densities
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CLT for crossings of random trigonometric polynomials
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The distribution of the zeros of random trigonometric polynomials
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Lipschitz-Killing curvatures for arithmetic random waves
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Fluctuations of nodal sets on the 3-torus and general cancellation phenomena
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Central limit theorems for the excursion set volumes of weakly dependent random fields
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Critical points of multidimensional random Fourier series: Central limits
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CLT for the zeros of Kostlan Shub Smale random polynomials
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Overcrowding estimates for zero count and nodal length of stationary Gaussian processes
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Roots of Kostlan polynomials: moments, strong Law of Large Numbers and Central Limit Theorem
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Fluctuations of Level Curves for Time-Dependent Spherical Random Fields
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