Variance asymptotics and central limit theory for geometric functionals of Poisson cylinder processes
DOI10.1214/22-EJP805zbMath1492.60028arXiv2111.04608OpenAlexW3211598722MaRDI QIDQ2149939
Carina Betken, Matthias Schulte, Christoph Thäle
Publication date: 27 June 2022
Published in: Electronic Journal of Probability (Search for Journal in Brave)
Full work available at URL: https://arxiv.org/abs/2111.04608
stochastic geometrycentral limit theoremintrinsic volumeBerry-Esseen boundvariance asymptoticsmultivariate central limit theoremPoisson cylinder processsecond-order Poincaré inequalitygeometric functional
Geometric probability and stochastic geometry (60D05) Central limit and other weak theorems (60F05) Integral geometry (53C65) Point processes (e.g., Poisson, Cox, Hawkes processes) (60G55) Random convex sets and integral geometry (aspects of convex geometry) (52A22)
Cites Work
- Unnamed Item
- Second-order properties and central limit theorems for geometric functionals of Boolean models
- Stochastic analysis for Poisson point processes. Malliavin calculus, Wiener-Itô chaos expansions and stochastic geometry
- Fine Gaussian fluctuations on the Poisson space. I: Contractions, cumulants and geometric random graphs
- Anisotropic Poisson processes of cylinders
- Functional Poisson approximation in Kantorovich-Rubinstein distance with applications to \(U\)-statistics and stochastic geometry
- Normal approximation on Poisson spaces: Mehler's formula, second order Poincaré inequalities and stabilization
- Random inscribed polytopes in projective geometries
- Berry-Esseen bounds and Cramér-type large deviations for the volume distribution of Poisson cylinder processes
- Stein's method and normal approximation of Poisson functionals
- Central limit theorems for Poisson hyperplane tessellations
- Central limit theorem for the volume of random polytopes with vertices on the boundary
- Normal approximation for stabilizing functionals
- A central limit theorem for the Poisson-Voronoi approximation
- Large deviations of the empirical volume fraction for stationary Poisson grain models
- Concentration inequalities for functionals of Poisson cylinder processes
- Quantitative two-scale stabilization on the Poisson space
- A Berry-Esseén theorem for partial sums of functionals of heavy-tailed moving averages
- Multivariate second order Poincaré inequalities for Poisson functionals
- Normal convergence of nonlocalised geometric functionals and shot-noise excursions
- Limit theory for the Gilbert graph
- Central limit theorems for \(U\)-statistics of Poisson point processes
- Intersection and proximity of processes of flats
- Does a central limit theorem hold for the \(k\)-skeleton of Poisson hyperplanes in hyperbolic space?
- Central Limit Theorems for Volume and Surface Content of Stationary Poisson Cylinder Processes in Expanding Domains
- Central limit theorems for the radial spanning tree
- Stochastic and Integral Geometry
- Translative and Kinematic Integral Formulae for Curvature Measures
- A limit theorem for statistics of spatial data
- Asymptotic properties of stereological estimators of volume fraction for stationary random sets
- Quelques théorèmes centraux limites pour les processus poissoniens de droites dans le plan
- Mixing properties of stationary Poisson cylinder models
- Random polytopes: Central limit theorems for intrinsic volumes
- Statistics of the Boolean model: from the estimation of means to the estimation of distributions
- Central limit theorem for a class of random measures associated with germ-grain models
- Asymptotic normality for random polytopes in non-Euclidean geometries
- Simplicial Homology of Random Configurations
- Moments and Central Limit Theorems for Some Multivariate Poisson Functionals
- Limit theorems for random polytopes with vertices on convex surfaces
- Lectures on the Poisson Process
- Convex Bodies The Brunn-MinkowskiTheory
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